I typically don't waste my time on anything less than a dual core as you can get them here in the USA as cheap as $10. I try to find something with Android 4+ which isn't too difficult nowadays either. If you are up in the air between two devices with same cores and such, go with the one with more RAM if there is a difference. most dual cores now have 512mb or 1gb. Internal storage doesn't matter a whole lot if the phone is dedicated because you wont need to update any of the other apps. However, most of them I get have 4gb+ internal memory and some even come with micro sd cards on top of that. Screen size and GPU don't really matter at this point since none of the BOINC projects utilize the GPU's in these devices. IF you do enough research, you can even find phones that are known to work without the battery being attached.

Now, keep in mind if you buy a cheap phone that some of them don't start their warranty until actually activated for phone service. This is how Net10 currently does their warranty. So, you have to fight them to get them to honor it if they are defective. Last I tried, it required a visit to the BBB and Tracfone (whom owns Net10 and Straight Talk) made good on the claim.

Now, I also use these phones for a few money making apps as well. So, they paid for themselves in a short period of time. So, I had a few other motives for what specs I was looking for.