Aftermarket speakers are going to sound better on a reasonable aftermarket headunit even without an amp.
If you have the money.. These are some great speakers that you can later amp up with a 50x2 (wouldn't cost much) if you wanted to down the road:
Focal Access - 165A1's -- 6.5 components. This is hearsay, not personal experience with them. You will find likely a unique response from most people who respond to this.
Focal Access 165A1 SG 6-3/4" component speaker system at Crutchfield.com
I'm not saying buy from
Crutchfield (good company).. but you can find them cheaper.
If you are adamant on not buying an amp,.. then just do your homework on a solid "clean" headunit. You don't have to spend a ton of money on it,... IE: It doesn't take a $750 headunit to sound clean.
In fact for $100-200 you can get a single din that will do the job.
There's nothing that difficult about amping speakers.. but it is pricey if you get a shop to do it.. HUGE difference.. markup is usually twice to four times what you can do it yourself.
Example I'm in the process of putting in a $2000+ system that the speakers and amp cost just over $600. For the equivalent setup and installation shops wanted 3 grand.
Also -- @mylows10 was right about the used. If money is SUPER tight.. I'd just go to the speaker classifieds and find the best pair of speakers in your price range. Used is generally 1/2 or less than new. Also, factory wiring will handle these speakers EVEN amped to their maximum 60watts RMS rating just fine if you DID want to grab a 2 channel amp. Example.. the PPI 600.2,.. Can grab around $100-130 (can find a 2 channel amp cheaper.. this is just an example)
PPI P600.2 Car Amp | eBay
I'm sure others will chime in here with speaker options.
Good luck,