Hi there! All great questions. This will be a heavily biased, lengthy post.
As others have said, you're walking into a drughouse asking for opinions about heroin. With that disclaimer, I hope it’s helpful.
First thing is that it sound like you’re interested in flying for flying’s sake. That’s key, in my view. The reality is that you have to really love it; it can’t JUST be about being more “efficient” for work or personal travel. If you take into account the cost of training, cost of purchasing a capable cross-country aircraft, maintenance, fuel, hangar, insurance, etc., you’d be surprised how close you get to "The NetJets Threshold,” which means that you’re almost at the point where you could simply buy an hours card on one of these operators. You can even buy an aircraft and then hire a commercial pilot to fly it for you; there are LOTS of businesses (and a few non-pilot individuals) who purchase piston twins all the way up to jets and do this exact thing. I knew a guy who purchased a 310, hired a pilot, and then decided he wanted to learn to fly it after a few years watching the guy he was paying up front having all the fun.
All that said, the great thing about aviation is that it’s a hobby that is ALSO really useful. There aren’t many hobbies that also have a real practical side about them. So, that’s all a long way of saying that it’s good that you don’t necessarily have a practical need to learn. In fact, if you came here and said “I need to fly 1,000 mile trips, monthly, in all weather, and I want to learn how to fly just so I can do that,” you’d be setting yourself up for disappointment.
You’re in almost the perfect sweet spot, though. You want to learn how to fly, and you also have some great uses for that skill once you develop it (more on that later). That’s pretty ideal. So I’d say definitely go for it. Go take some intro flights and see what you think. Definitely take your time picking a flight school. There are a
lot of lousy flight schools out there. Talk to the CFIs, talk to the owners, and TALK TO STUDENTS THERE. I can’t emphasize this enough. We lose so many promising students to bad schools. Better to drive an hour to a good school than 15 minutes to the closest-but-lousy one. The kinds of people who want to run flight schools love flying airplanes (or working on them) and often are terrible at literally everything else: business savvy; customer service; often instructing itself—everything. It’s just reality.
Also—and this is key for you—ask about their rental policies once you get your ticket. You want a place that lets you take the plane overnight for a least a bit of time. This won’t be a long-term thing; ultimately, you’re going to have to buy or partner into a plane. A club might be an option but probably isn’t if you’re really looking to travel. Early on, though, it’s nice to have at least a decent rental option so you can start feeling things out without a huge capital expense.
Once you get your ticket, that trip to St. Louis will be great. You won’t be able to get everyone into a 172 (typical rental), but you could fly your wife and maybe the kids—and the dog stays home and Mom takes the airlines. Or some other variation. Maybe the first couple times, you just go solo and meet them all there. Whatever; you’ll figure it out, and it’ll be loads of fun. You’ll be pretty limited on weather, so if you absolutely NEED to get there, buy some refundable airline tickets just in case. But you’ll be able to make some really fun trips, especially in the summer. Cost is probably around $10-$12k to get the ticket and then a couple hundred bucks an hour to rent, likely with some minimum number of hours billed for every night the plane isn’t at the home base.
If that seems cool, then next up is the instrument rating. After a bunch of trips to St. Louis, you’ll have all the prerequisites needed for the IFR work. That rating is another $10k—pretty much whatever your private cost, maybe a bit less. At this point, you’ll have a good sense of whether this is for you, and you’ll have learned a lot about things like useful load (i.e. how many people you can actually carry in a given airplane and go a given distance), how to analyze performance charts, how to haircut the manufacturers’ BS on advertised speeds and range, what weather you can really tackle in something that isn’t an airliner, etc. This is a fun time, and you’ll probably start looking at getting your own ride.
Airplane costs are all over the map. Like cars, aircraft depreciate heavily after just a few years. The difference from cars is that there is ALWAYS a more capable plane for the same money, used. So you’ll get a lot of people who just look at you like you’re crazy for buying new. With cars, it’s always “you’re paying X amount more for new,” but with planes it’s more like “for that price, you could get a jet!” Anyway, this is all stuff you’ll learn as you gain more experience and talk to other pilots, and there aren’t any right answers. At the higher end, operating cost tends to become more important relative to acquisition cost.
I’ll give you a few quick-and-dirty data points just to help you calibrate (I’m not actually recommending any of these airplanes; I have no clue about your budget or a million other variables that matter). A brand-new loaded Cirrus SR22T is around $800k and probably costs around $200/hour to operate. Seats five (it’s VERY tight with five: you need to leave off fuel, and your passengers will probably hate you). It won’t carry everything you want to carry, but it’ll do most of your trips pretty nicely except Boise; you’d absolutely need a fuel stop for that one, and at that point, you’re really losing ground to the airlines. Not that it can’t be a lot of fun to fly yourself on some really long trips, but in terms of efficiency, time, (and money, but you almost always lose on the money front), the airlines will win.
Another data point: my plane. Acquisition cost was about $430k, and it costs me around $500/hr to operate including engine reserves. By the way, the manufacturer has a nice cost breakdown here:
http://aerostaraircraft.com/Super 700 Operating.pdf. Obviously, it’s just for my plane, but it should give you at least a sense of the categories you should be considering for opex. It’s also pretty honest compared to a lot of these I’ve seen from others. My costs are higher than book because I live in an expensive area of the country (Seattle) and fly into expensive areas, including The People’s Republik of California, where fuel frequently touches $6/gal.
Jam-packed, it’ll carry seven, and two of them had better be kids (kind of like the Cirrus with five). Real-life, five people are very comfortable. Five people and a non-miniature dog would be pushing it. All of those trips would be doable, but Boise would necessitate a fuel stop on whichever leg was seeing a headwind. With five adults, even the 700NM trips might be pushing it because I couldn’t carry full fuel.
Now, let’s jump up to an aircraft that would really do that Boise trip with no sweat: a nice, 10 year old CJ2. Friend of mine has one, so I know it pretty well. It’s around $2.5mm to acquire, and including engine reserves probably around $1k/hour to operate (but at 400 knots, you’re 60% faster than I am, so it’s not as bad as it sounds). It would carry your entire passenger load (and the doggie) in pretty good comfort, and it’s got a potty (not airliner-quality, but good enough for emergencies). An older King Air would do it slower and for a lot less in acquisition cost but probably about the same operating cost (per trip, not per hour).
Now, for the jet, you’re going to be investing a lot in training. Even something like my plane isn’t a good option early-on; you’re just having to learn so much at once. I’d think a plane that can do 100% of what you want is seven figures in terms of cost and a few years out in terms of experience if you’re flying a lot and are willing to hire a mentor pilot to come with you for the first 50 hours or so in the plane (and when you’re spending seven figures, this really shouldn’t be too big of a deal). The single-engine turboprops might be a good play, too, and will have really appealing operating costs relative to the King Airs and jets. PC-12 is slow and carries a ton; TBM is fast and carries quite a bit less. If you can compromise on how many people you’re taking along and don’t mind taking the airlines for the longest of your trips, then you’ve got plenty of single-engine aircraft to choose from and a ton of piston twins. The bigger piston twins will carry everything you want, but your Boise trip will still be a stretch. Keep in mind, too, that as you move up in performance, your number of usable airports decreases. I’m flying with family to Oregon on Friday, and there’s a 2,900' strip literally five minutes from where they’re staying . . . which would be swell if I owned an SR22. With three people, my balanced field length is about 4,000', so the time I save being 40% faster than the 22 gets more than eaten up by having to land at the less convenient airport. Everything’s a tradeoff.
Anyway, I hope that’s a helpful overview of where things are going. My advice: start small, doing that St. Louis trip in the summer in a rented 172 and gradually building up. Unless you’re an actual billionaire with your own BBJ, you’re never going to do every trip in your plane. I’ve been eyeing the CJ3 for a few years now, and even if I did buy that someday, I would still take the airlines for my Seattle to JFK trips (and even in first class, I'd be saving
thousands). I don't think an airplane exists that is single-pilot certified and can do coast-to-coast nonstop. I’ve flown as a passenger in a G-IV from Philadelphia to Innsbruck, and I’ll probably never do it again; business class on Lufthansa is about 5x more pleasant and (literally) 10x cheaper, even accounting for the TSA groping.