OP: I think your heading in the right direction. For the styles you mentioned and your budget..... I think you can't go wrong with a Fender P or Jazz. In fact, I'd recommend a P/J which has the Precision P/U's near neck and the Jazz near the bridge. I would NOT do a squire for numerous reasons, and to name just a couple, the electronics and p/u's are far inferior to even the MEX Fenders. Also, if you look around, you can get a decent Mexi for the price of a new Squire.
Here's a couple I just saw......
Look up these on ebay. Place the item number in the search: 160405776767 or 150418149717
.... these new are about $650.... so $450 or so for a great condition one is a good deal.
the Jaguar's are really cool to but are going to be harder to on the c-list if you're looking for a good used deal. If you "know" this one is for you, go for it, but you can't go wrong with the P's or Jazz.... or P/J.
pay the 100 or two extra for active electronics. TRUST ME! especially if you aren't playing through some serious high wattage gear, you'll miss the low-end and fullness active p/u's can give you, plus you can always roll the preamps down to make it passive (or a combo or each).
As for amps.... Look for a good deal on craigslist. You can always find say a GK Backline 1x15 for under or around $200.... but I've got a feeling you would outgrow something like that soon, playing with drums, etc. Good for starters would be something like an Ashdown MAG Combo, the 410's or the 115 are nice.
Now to retract.... I would definitely pay for the American made models and buy the bass, then amp as you can afford them.... but I will admit, you can find some gems with the Mexi's and then always upgrade the p/u's if the build and playability are solid.... once you become "one with it"
Couple other random notes, I wouldn't get cheap with cables. try the "Monster Bass" instrument cables, fuck all the whine about Monster, they are badass cables...... spend $30-50 on a good cable or two. The monster bass kinda curl and twist after lots of moving, but worth it. You could have all kinds of decent sound with a cheap set-up and kill the potential with shit cables.
If you're not into the tech stuff, pay someone (reputable) to do a professional set up for you (60-120 bucks).
good lucks!