Welcome and congratulations. Excellent choice.
Manual or automatic? If it's an auto--and especially if you're going up to 33s--your first mod should probably be a superchip flashpaq.
Putting that aside, 33s that are the same width as your current tires will fit your stock Jeep, though it'll impact your mpgs a bit and you'll want to recalibrate your speedometer. So no, you don't need spacers or a leveling kit. And unless you're going to add a tow hitch and use it a lot, I don't think you'll need a gear change for 33s.
Also, as to the Spidertrax, I'm getting them on my Jeep next week and am really excited. However, I wouldn't be getting them if I wasn't so in love with my stock wheels (Mountain edition). It's just a better practice to get wheels with the proper backspacing in the first place. I know you mentioned keeping the stock wheels, but if you're not crazy about them you might be able to work some new ones into your budget that obviate the need for spacers at all, particularly if you're not doing the leveling kit either.
I'm not a tire guy, so I can't really help on specific recommendations.
I will note though that there are other mods that can help with an "aggressive" look. Knobby 33s will help even without a leveling kit/spacers (though the knobbier they are, the worse your ride and mpgs will be), but you may also want to consider a grille guard or stubbing your bumper, tail light guards, supplemental lighting, decaling, or body armor, among other possibilities.
Truthfully, my real recommendation would be to drive around for a while, maybe do some wheeling, engage with this forum a lot, and then decide. There were things I "knew" I wanted a couple of months ago that I know now would've been stupid. Just enjoy your Jeep for a while and then start making these decisions.