A lot to ponder for a 16/17 yr old. When I was your age, I got the hand-me down 71 Dodge Dart from my dad. It had the 318 in it and I used to smoke his snow tires consistently. I didn't realize I was to purchase a new set. He wondered how he was able to last on the tires through 4 winters and I only had 1. Then the cost of a v8 for gas mileage just sucked. To add, teenage years is all about competiton.....like you stated, your buddy has something that is claimed to be what you want. No not really. Like others have stated, compromise is best for you. School should be where your head should be. Grades to get into college, college to get a job, job to get a life to enjoy and have fun. Spending as little as possible now to reach your goal is best for you. Get things for the Jeep to perform is what you would want rather than the 'Bling' to what it looks like.
Not only does adding stuff cost, but so does maintenance. If you are mechanically inclined and can perform the work, the better you are off. I've purchased many a things used for my TJ over the past couple of years.
So what you should be looking for are used items from those upgrading. I'd weight what others have stated here, talk to your Dad (appears to be goal oriented), set some goals to accomplish, and take him out for some fun.
One of the biggest things I'd suggest would be to look for a local 4wd club to join. Knowledge is best shared as well as parts. Most clubs won't allow a teen to join so you may have to get your Dad or older sibling to join also.
For a budget build, keep things simple. Tire size is not all what gives offroad. Its a lot dependant on the driver and the capabilities of the vehicle. Short comings of the vehicle will be learned by the driver, that is why we always spend and look for upgrades. Safety and recovery items should be a high priority, including self extraction- hi-lift, straps, clevises, frame attachments, first aid, cb, etc.
Next could be aggressive tires. Look for something that will fit on the stock rims to be cheap. Depending on how much trailriding you do, aggressive ATs would probably suffice. Tire size plays a big part in the performance of the vehicle, so keep it large and small at the same time. Others have given you an idea on the performance changes with larger tires, so there is always added costs to larger tires. To fit, YJs can use TJ flares to open the wells more, longer shackles do help to get that extra space, and by adding quick disconnects to the front sway bar, you can get better travel. Some suggested to remove the track bars, but most of this weighs on the driver. Some YJ drivers prefer it, some don't. A track bar is the bar that attaches to the axle at one end, the other end attaches to the frame. Sway bar connects to the axle at 2 points, and the frame at 2 points. You'll be best to keep the sway bar attached for streetability.
Shocks help the ride, so you could consider this a maintenance item without going to a 'lift'.
Body lifts are another way of getting necessary clearance for larger tires, but if you keep the tires relatively small (31-32's), then combination of flares, shackles, and body lift would work. If you do decide to go with a 33, keep it skinny at 9.5". These fit on the stock rim and with the combination 'lift', you should have enough clearance for them. I know of a KCJeeper looking to sell a set of 33x9.5 AT's (
http://www.kcjeepclub.org/forum/viewtopic.php?t=7864.
Good luck and let us know what you go with.