I'd say the amp #s from that amp LIE.
Lots of companies lie about wattage just Google it.
Alpine lies less generally speaking.
Also that amp does not state RMS wattage, just max wattage.. I even downloaded the manual PDF and checked.
A lot of people mistakenly believe that it's all about the numbers on the box. Its not. Companies lie all the time.
My 10 year old harmon kardon 5.1 stereo is rated only 65W RMS x 5 and yet it sounds louder and clearer than the Yamaha I bought which is "rated" (lol) at 100W RMS x 7 on the box. I returned it.
Go with a good name brand amplifier, not a Chinese knock off.
Yeah, for speakers, ignore the numbers and go with reputation. And BTW, for rear door speakers, don't spend much if anything. I got a pair of 2-way pioneer 5.25's for $26 on amazon, they get great reviews. Don't bother with the $77 pair linked above.
Also, if you are just looking for value, I think the single best value you can get is not new speakers, or a sub, but it's the head unit. Get a decent aftermarket head unit first. You can get an excellent Pioneer HU with all the bells and whistles you need for $150 or less depending if you want HD Radio or Siruis. After that, get new 2 or 3-way front speakers, those references are probably fine (I got a great deal on some pioneer 3-way's years ago, so I run those). As folks have said, also replace the speaker wire. You can use cheap CCA wire from wal-mart or something like that, so a big spool for about $15. CCA is fine for speakers, not ok for a sub. Add a car door adapter for $20 for the 6.5's, and you have a totally decent system for under $300.
If you want more, then you should look into a sub and dedicated sub amp. The advice here on that I think was pretty good. Go with class D, it is way more efficient. Again, don't worry alot about the numbers, just be sure you pair an amp and sub with similar numbers. I have alot of respect for Alpine subs after torture testing some at work. I run an old JL audio amp and it has been solid for about 6 years (even got rained on once...).
Then the last thing you should buy is an amp for your speakers. If you replace the HU, then the new HU should have an internal amp up to 40-45W, which is plenty. I eventually got a separate 4-channel amp (again, class D), but it wasn't really necessary, probably not the best use of my Christmas gift... oh well. I used the HU internal amp for 6 years and was totally happy with it.