Warning: long post!
I pretty much only use/recommend Rockford Fosgate in my systems. Stock speakers are pretty weak and will melt the voice coils in a short period of time with an amp hooked up. If you are going to run a 5 channel amp you would need 3 inputs for them (Front,Rear,Sub) so honestly it would be better to get a cheap head unit with an aux input.
If you are going to amplify your stockers just be ready to replace them. If you tune them properly you could make them last a little while but they will pretty much sound the same, so whats the point? New speakers alone will sound much better than amping up your stockers.
Most of your Ipad to RCA converters will only have one set of RCA (right,left) so one channel only unless you use a couple of splitters to each channel. A sub is going to need its own input but hooking up full range to a sub (even if it has a low pass filter) will sound muddy.
1. For only an Ipad get a couple of amps. Ipad to RCA with a splitter for front and rear channels. A 4 channel amp for front and rear speakers with RCA input AND output so you can pass through to a sub amp. A couple of crossovers for the front so you can keep your in dash tweeters. You could do this with the 5 channel amp and use multiple splitters.
2. Keep your stock HU get some RCA converters for the speaker wires and hook up your amp or just the sub amp. Use the 6 disk input (if applicable) to your ipad with a converter.
3. Amp with HU. I would do Rockford Fosgate 5channel 1000x5 a good base for later upgrades
http://www.rockfordfosgate.com/products/details/p1000x5, with a cheap single DIN small head unit you can recess or hide some where that offers Front Rear Sub and Aux inputs for your Ipad hookup... (Walmart or Craigslist, Secret Audio<google it). That way you could do your ipad dash. A little pricey but worth it in the end.
My current set up is a cheap Valor touch screen HU with Navi to the stock speakers. With a Rockford Fosgate Monoblock amp 650RMS and two 10" punch P2 subs. Cheapish and easy, plus i can hook up my ipod/phone/usb stick/SDcard or whatever to it. Plus I love my reverse camera. When these speakers blow I have an RF 4 channel amp in the garage, gotta get the front and rear speakers still though.
Crappy pic of Valor HU
Here is my buddy's system that I did in his 05 Accord. Sounds AMAZING! He spent about 3k (including my labor costs
) decided not to use crossovers and kept the tweeters hooked up to the HU bypassing the amp.
http://imgur.com/a/ZQW9M
Sorry I got carried away. Ill come back and edit later...