the first basic need to run linux is , some amount of RAM with MMU. it not a good idea to select a random processor and try to port linux on.
we need some already supported processor with decent latest version of Linux available. and some community support will also do.
the first issue you will face in choosing right processor is the package , almost all somewhat latest processor which support Linux comes in Large BGA (>200 balls)package. and doing BGA on low Cost at Homemade stuff is somewhat pain.
Large BGA require specific soldering equipment , you need some sort of oven for large BGA. hotair will not work very well for BGA larger than 200 balls .
and BGA witch pich less than 0.8mm require PCB with very fine pich.
common low cost PCB specs are like 5mil trace / 5mil clearance , 10mil drill 4 mil annular ring. if you are going more finer that this you may need to pay lots of amount of money.
to fanout large BGA we need to place via between the pads, for that we need as low as possible clearance , minimum drill , as low as possible annular ring. minimum 4 Layers are kind of must of small BGA , you really don’t want to do less that 4 layers, 6 Layers or more is recommended for large BGA .otherwise there will be lots of issue with fanout and power rails.
but i want to whole process at minimum cost and all at my Home.
so i need to leave BGA behind for the processor and consider some large TQFP or QFN package for processor,
but there are handful of modern processor available in TQFP package which run linux, so we have to chose from them ,
one very common choice is freescale iMX233, which available in TQFP128 Package ,ARM9 running at 400 Mhz , has LCD, audio, USB Host, everything we need.
or we can go for Allwinner A13 processor , it is in TQFP Package , ARM Cortex-A8 running 1Ghz, has LCD with Mali 400 GPU, has one USB device and USB host, support two SDcard or NAND flash, support upto 512MB DDR2 or DDR3 ram.
for some reason i am looking for faster processor with more of everything so i chose Allwinner A13 , as it is only learning project we really don’t care much about how the processor is available for sale etc. i have experimented with Allwinner A20 processor before ,i found them to be stable and easy to use, sunxi linux repo on github has very stable linux 3.4 branch , and underdevelopment linux 3.10 branch.
sunxi linux 3.4 brach support most of the stuff including GPU which is nice .