Put the dog on the back seat. I found that my dog is more comfortable in the back of my Arrow and she was going to interfere with the yoke in the front seat. The short-body PA-28 is a great plane for one or two people and up to one dog. I occasionally use the back seat for people, but rarely.
This brings up another question.
The annual, which is also called the 100 hour, MUST be done once a every 12 months or every 100 hours, which ever comes first... is that correct?
The overhaul is optional or how does that work. Does not doing it mean you cannot take passengers until done?
The plane is not airworthy for any flight unless it has had an annual inspection within the preceding 12 calendar months. That applies to every certified airplane. The annual must be performed by an A&P with an inspection authorization ("IA"). If the plane does not have an annual inspection within the time limit, you are legally required to get a ferry permit from the FAA to fly it at all.
The plane cannot be used for hire to carry passengers or give flight instruction unless it has a current 100-hour inspection. (That does not include you getting instruction in your own plane; it mostly refers to flight instructors who provide a plane to the student.) This inspection can be done by a non-IA A&P. Because an annual inspection covers the same ground, it's common to see an annual inspection sign-off that says it was also in accordance with ("IAW" in A&P-speak) a 100-hour inspection. But if they left that off, the plane would still be airworthy for uses that do not require a 100-hour inspection.
The engine and propeller overhaul limits are mandatory for certain operations, which do not include flying yourself around for fun or receiving flight instruction. Sometimes an engine will go long after TBO. Sometimes it will only go halfway to TBO. The reasons for both outcomes vary wildly, from not flying enough to flying too much or from running the engine too hot or not hot enough. For personal use, the TBO number is really just a guess. You overhaul when needed based on other things. If the engine is consuming a lot of oil and the compressions are low, overhaul it. If the propeller has huge gouges out of the blades or is a constant-speed propeller that is throwing oil from a blade seal, overhaul it. If a plane you are looking at has been flying regularly since its last overhaul and has not been abused, then you can use TO to decide how much to offer for the plane, based on a reasonable guess about how long it will fly until you have to pay for an overhaul.
Ideally, I'd like to do a cross country flight after I get my license. Connecticut to New Mexico, where I have some family.
Would this plane be able to make that trek and back in one piece?
It depends much more on the pilot than on the plane. The most important skill to develop is good aeronautical decision making (ADM). With a longer trip, you need to consider more things like where to stop for fuel, how to avoid bad weather, what to do if you run into bad weather despite your plan to avoid it, etc. For example, the distance from Bridgeport to Albuquerque is 1,617 nm. At this moment, the conditions in the Northeast are IFR with low ceilings. You would have to wait for some improvement before you take off, unless you are instrument rated and current and flying a plane that is certified and current on inspections for IFR. Along the direct route, you would run into heavy precipitation over Ohio and thunderstorms from Missouri to the Texas panhandle. If you divert south a bit via Little Rock and Lubbock, you add 100 nm to the trip but go around the major weather patterns. You still have IFR conditions to contend with in Texas but not thunderstorms.
I don't know the range of a Cherokee 140. It's probably between 400 and 500 nm with full fuel and a legal VFR day reserve. Let's call it 400. One plan with legs that long would be to stop in Spencer, WV (KUSW), Trenton, TN (KTGC), Sherman, TX (KGYI), and Lamesa, TX (KLUV). That gives you three legs of ~400 nm and two legs of ~270 nm. With no wind in a 110-knot plane, it's 3:40 per 400-mile leg and 2:30 per 270-mile leg. Total time in flight is 16 hours. Add time on the ground at each stop to stretch your legs, have a snack, check the weather (basically you will want to re-plan the entire remaining portion of the trip at each stop, so you can adjust to any changes in the situation in front of you), fill up the fuel tanks, and preflight the plane again, and you're up to a minimum of 18 hours en route. It's not sane to do that in one day. It could be a nice two-day trip if you are up for it and flexible about weather or fatigue making it wise to stop for the night before continuing.
With good planning and flexibility, it can be done. There aren't even any troublesome mountains along that route. You have to cross some low mountains that are still a hazard for the unwary and that can make their own weather, but you won't have to cross mountain passes at the service ceiling of the plane. People have flown slower, less capable, less comfortable planes on trips like that since before the advent of the attitude gyro, much less the GPS. And it sure beats driving for 30+ hours. But it's not something you'd do for the purpose of being at the destination. The $342 commercial flight that takes 5:25, suggested by Google Maps when I checked the driving distance, is how you get to the destination. You fly a trip like that because you simply love flying.
