This is how I would do the job:
I would use PIC18F1320, which has 18 pins.
The trial version of mikroC pro for PIC compiler should be enough to write your code for free.
You would need a MikroElekronika programmer, costing about $100
You would need IR LED(s) and driver transistor, plus a couple of resistors.
There are many other ways to do the job, many better, but this just suits my amateur experience and tools I already use.
This would make a poor remote, as power consumption would be high, and either an on/off switch would need to be provided to prevent using power when not in use, or a more complicated design would be needed, using 8 diodes to power up the PIC whenever one of the switches is pressed.
I am not experienced in programming for low-power operation, so you would be on your own with that.
It is for the above reasons that I usually use an existing remote control, where all the above problems were solved by the remote manufacturer.
There are cheaper PIC programmers around, but again, I cannot help with those.
I can help with PIC programming for IR, but only at amateur level.
Buying a hobby kit would be cheaper, since the chips come ready programmed.
My favourite site for explaining IR protocols is here:
http://www.sbprojects.com/knowledge/ir/index.php
Sony protocol is the simplest.
Some of my complete IR Tx/Rx projects are here:
http://www.libstock.com/projects/view/43/infrared-tx-rx-samsung-sharp-nec-sony-rc5-rc6-mce-toshiba-ir-easypic7-pic12-mmb18-mmb33-arm
You will find 4 button transmitter and receiver using Sony protocol and 8 pin PICs