Agreed. Get a good HU and leave the stock speakers if that's all you can afford. Buy a nicer used HU if you can't spend enough for a good one. Heck, I just picked up a mint condition Alpine CDA-9833 for $100 that includes 6-channel T/A, crossover, 5-band parametric EQ, V-Drive internal amplifier, etc. My 2002 Camry has had stock speakers and aftermarket HU's ever since we got it (mostly because all my time is in the Accord).
The CDA-9833 gives me extra control in that car... however aftermarket component speakers are planned very shortly (just sitting on a shelf anyway). that car will have front and rear because our children like to have music also, but we use our fader as needed to control levels.
The installation of aftermarket speakers requires extensive effort in order to achieve proper results. This includes fabricating baffles, sound deadening, foams, etc. as i've outlined in a sticky in this section.
Speakers should always be upgraded front first. the front speakers are what you hear the most, music should come front in front of you. You're going to want a component set and you can start by locating the new tweeter in the factory dash location, or move it to a location you like more (like the apillars).
Rear speakers are for low end or rear fill only. They should not be the dominant source of music. Most manufacturers use larger 6x9's in rear for bass only - there aren't tweeters back there for a reason. tweeters behind you are pointless. Upgrade your rear speakers only after you're happy with the front sound quality.
No stock head unit will adequately power aftermarket speakers. Factory speakers are very efficent, aftermarket speakers are not. Factory amplifiers are very small with high distortion. Many people are happy after a simple HU upgrade. Your 2002 has the same factory system as mine did, and as my build log shows, i'm very familiar with the vehicle. I did use the factory HU to feed a signal to an audio control EQL then to an xtant amp which ran my front components and a sub. That was an acceptable system.
If you can't afford amplifiers AND speakers, your best bet is a new head unit. you can power aftermarket speakers from an aftermarket head unit. you can power factory speakers from an aftermarket head unit. i NEVER recommend powering aftermarket speakers from a factory head unit. if you must retain the factory HU, add an amp and LOC to power the speakers. There are a lot of factory integration pieces out there to facilitate this with integrated head units. the 2002 is not integrated and easy to remove.
That said, the only way to get true performance from aftermarket speakers is with a quality amplifier and a rock solid installation. the difference is amazing, and only those who have experience it (with above average equipment) can actually comment on the benefits.
Alpine, JVC, MTX, Rockford are all mid-grade equipment. Hybrid Audio Technologies, Hertz, JL Audio, Focal, Morel, all make good "entry-level" speakers, but "entry-level" for them is well above average from your everyday BestBuy brands.
sonicelectronix is not an authorized seller of most of their brands (except they are for Powerbass). Crutchfield is an authorized seller and they will help with install kits, wiring harnesses, instructions, etc. for the newcomer. But before you buy online, look at local shops, talk to installers/sales, etc.
For new head units, Pioneer, Kenwood eXcelon, Alpine have good budget units. Personally, I think the CDA-105 is a nice starting piece, as is the Kenwood KDC-X794. Make sure to review each unit with the desired adapters you want (ipod, sat radio, HD radio, USB, Bluetooth, etc.) to verify if you need to buy extra peices to acheive your goals.