This bass is somewhat heavier than a Jazz Bass, and can be somewhat large and long, but it was never too awkward for me to handle, and I'm less used to playing bass than most. A well-maintained P-bass will play and feel great, and the top notes won't be too far out of reach for anyone. If anything, the lowest notes will be more strenuous for someone with shorter arms. Everything on this bass is smooth and stable.
I like using this with a Peavey tube bass amp, but I've heard many good combos with it. I like a nice, smooth, fat tone, one that isn't gonna pop too hard, but fat enough to hold down a heavy groove. This bass is definitely more low end thud than the J-basses smoothness, but it has plenty of both. It's pretty versatile and can really hold down a fat groove. Distorted, it is particularly nice because it doesn't get too fuzzy, and it doesn't lose the pop of the low end. I really like using this for rock music, as well as some of the heavier funk and R&B. Most of the rock I play isn't too heavy, more in the vain of Dire Straits and Wilco in terms of heaviness and dynamics, and I think that the bass is just deep and round enough for those genres.
The old P-basses, in my opinion, are some of the best instruments made in the 20th century. These will certainly cost you a pretty penny nowadays, too. Getting a good used one is a good lifetime investment for the true bassist. I think it's worth it in the long run, before they get even more expensive. They sound absolutely phenomenal, and if they are well-maintained, they play great too. The P-bass is certainly in a league of its own, and going classic is definitely the best choice.