I would stay away from the Alpine Type S speakers. I've auditioned them, and find them lacking in the midrange. I compared the Type R and the Type S speakers at Best Buy, and found the Type R speakers to be less harsh and have a more even frequency response. I would also recommend the Type-X components though. If you are on a budget, I think the Type R SPR-17LP is one of the best value speakers on the market. It's a time coherent alignment between the woofer and a tweeter, thus creating a fairly symmetrical radiation pattern for the entire sound spectrum. Try to stay away from any oval shaped speaker (5x7, 6x8). Oval shaped speakers have less cone rigidity than round speakers, meaning that oval shaped speakers exhibit higher levels of distortion (also uneven sound radiation).
If you don't want to cut out baffles for circle speakers though, I've personally auditioned these 5x7's: Polk DB570, Boston S75, Boston SL80, and Infinity REF6812CF. These were all auditioned at the same store (Sound Advice in Sarasota). I preferred the Boston SL80 first and Polk DB570 second out of the bunch. Boston SL80's are smooth sounding speakers. The Polk DB570's are a little heavy in the midrange, but otherwise sounded better than the rest. The other two speakers sounded harsh in the treble region and lacked in the midrange. To be honest most budget speakers will lack midrange because cheap speakers usually have cheap crossovers.
Add a set of super tweeters (10khz or so up) in the front pillars, and you've got a nice budget setup. I'm using the SPR-17LP's right now with the P5 stock tweeters. People complain that the stock P5 tweeters suck, but little do they know they are actually a super tweeter setup that are made in Japan.
Also, if you are keeping the stock HU, keep in mind that it is designed to bass heavy. I posted a while back some graphs on the response curve of the stock HU.
Tube designed subs are very good speakers, look around audio forums for sonotube built subs. Problem is the bazooka sub design uses plastic as the enclosure. This makes for the "cheap sounding" comments that I hear from a lot of people. I've heard bazooka subs, and I agree that there are better values for your money. They are the classic auto sub: good SPL, bad sound quality. I haven't heard many auto subs, but Vifa, Seas, and Peerless have some pretty decent subs (unsure of box volume requirements though).
Car amps are a total crapshoot in the budget range. You get what you pay for in the amp category moreso than any other car audio component. Stick to reputable brand names and you will be fine. MTX, Zapco, J/L, JBL, etc. Whatever amp you choose, make sure it has a CEA-2006 rating. This helps ensure you get the power you paid for. I know J/L does not use the CEA standard, but that's the only exception I can think of off the top of my head.
If you wanted to stay with just ONE brand, I would say Aurasound. Some of their stuff is hard to come by, but they had good sounding stuff: from tweeters to subwoofers to amplifiers. Hope this helps.