I'm partial to the CJ-8's as well, but if I had to choose between a 7 and a 5 like you do, I'd chose the 7. If you're looking to get into it right away and spend a lot of money on mods, do whatever you want. If you're looking to save money this is what I'd do.
You said you already have the 350, so let's start there. I'd get a running CJ-7, from '78 to '82. The '78 is the earliest I'd go due to the ability to upgrade the heater box ('77 was an option, or was it '76?) and the front disc brakes. The '82 would be the latest I'd go due to the addition of the cat and all the emissions crap. If possible, I'd stick to before 1980, which is when the 5 bolt hubs (weaker than the 6 bolts) came into play. The only tranny worth a damn in the 80's was the T-176, but the T-150 3 speed only had a 3:1 first. Anyway, get the jeep first, and make sure it runs well. While you're driving the jeep in it's stock form, gather the parts for the mods you want to make. It'll take time to decide EXACTLY what you want, you'll probably change your mind more than once. When you have the parts, do the mods.
I did this and learned a considerable amount. I bought my Scrambler for $700 and it was a piece of junk. I got it running and on the road, wheeled with it for a year while I gathered parts from many different sources. Finally I swapped them in when I had everything together. Keep in mind if you do it piecemeal it won't hurt as much and you can take time to do it right. Not having the cash on hand, I swapped out the SR-4 (junk)and D300 for an SM465 and NP205 (Which I bought complete for $250). No adapter needed as the GM151 (4 cyl offered '81-'83) has the same bolt pattern as the 350 (but you already have the engine). New driveshafts and I'm on the trail. At the same time I swapped in a pair of Scout II D44's that I had lying around. They can usually be had very cheaply and parts are reasonable for them, also very common. The stock axles will hold for while if you go to the 1-piece rear and are easy on the throttle.
I know of people who have awesome jeeps and still can't drive worth a crap. I'm not saying this applies to you, but I learned a valuable lesson from it. When I started driving off-road (oh, so many years ago), I thought I knew how to drive. I was wrong. By driving a stock vehicle I had to LEARN how to drive well, so when the mods came, the toughest obstacles were a breeze. I'm doing the same with JEEPNCHICK and her '47 CJ-2A. It'll be lifted 2.5" but open on the axles until she learns how to drive it well, then it'll get locked and modified. Remember, we'd all like to get up and run a marathon, but have to learn to walk first.
Good luck with your decision.
JEEPN
'81 CJ-8 Scrambled!
GM151/SM465/NP205 twinstick/7"Lift/33"TSL's/IHC D44's 4.10's Lock'd