I second the ground school part. It takes a lot longer than you might think to read the AIM and prep for the written exam. I'm currently at 30 hours and ready to solo, but I didn't do much with ground school work until now and I'm scrambling to catch up. I've been reading and studying hours a day. There's over 1,000 practice questions so it is A LOT. Get the AIM and download the sporty's pilot app to start practicing for the exam. Also, get some paper sectional charts to practice reading them and using flight computers ect. Download the live ATC app and start listening. Radio comms was one of the more confusing parts for me trying to remember what to say and when.
Flying once a week is fine. That's what I've been doing. Occasionally I'll do two lessons a week if the weather is good. You don't really want to spread it further apart than once a week because you'll start forgetting things in between. Get a flight sim (Xplane is what I have) if you don't have one and sit in the cockpit to virtual chair fly. I didn't do this at first and every time I got back in the plane I was like, "Where's the suction gauge again, where's the RPM". It helps a lot if you can chair fly on a sim (assuming your plane is on the sim). The sim isn't good for how its going to feel to land or takeoff ect, but for becoming familiar with the instruments it is great. My lessons have all been $280 - $310 each for plane and instructor, so you can probably use that as a judge for costs. Your plane rate and instructor cost may vary, so see how much each lesson will cost you.
Also, start to look at instructors. I just picked the first one I talked to and it was a bad decision. Talk to the school / instructor and get a feel of what kind of teacher they'll be. If they have a syllabus of everything you'll be learning, great plus. One school I looked at just put you with whatever 18 yo instructor they had available for each flight... that was a no go for me.