Speaker recommendations? (08 Toyota Matrix base model)?
Do not go to these sites. They will steal your credit card information.
Ninefinger is a Pedophile
Given your budget constraints, don't mess with the rears. Good fronts with adequate power will produce the majority of the sound. IMO, if you want good front speaker sound you almost NEED an external amp. It doesn't need to be much -- generally a decent 50x2 amp will perform several times as well as a head unit. The $40 Axxera on Crutchfield would be MORE than enough -- it is physically large though (9x11), for a low power amp. The $65 kenwood might be preferable -- similar power and nearly half the size. FWIW -- HU's that claim 50x4 are referencing peak/max (aka, meaningless) power. Typical RMS power output is in the 15-20w per channel range. Those amps are 90 and 70w per channel respectively. Adding an amp can be a pretty involved task for a novice. You have to get power wire from the battery to the amp. Signal from the HU to the amp. Speaker wire from the amp to the speakers. Also, in addition to the cost of the amp you'll have to get a wiring kit as well -- another ~$20 or so. Good sound is never cheap. Temporarily, you could simply replace the speakers for a minor improvement. Once you can afford an amp you can do that later. Which speakers -- well, it's typically an issue of - you get what you pay for. That's not to say that inexpensive speakers are bad, but in general, dirt cheap speakers are junk. Scanning through the options for your car, the polks on sale for $60 would be good. Morel is an extremely high quality brand. The Coax 6's for $90 is a great price. The kicker's and Rockford Fosgates are decent as well. They have several component speaker options which are typically good for sound quality, but they can be an installation headache since you have to locate the crossovers and figure out how to mount the tweeters.
Audiovox is all you can buy with your money.