If you are purely out to learn, consider mining testcoins (the bitcoin clone that is exactly identical except for running on a different port and being considered worthless by popular consensus). There you can even easily mine without needing any pool.

If you do insist on working on the Bitcoin port, really just about any pool should still allow you to participate. The question might be, though, what mining software is appropriate. If your choice involves downloading the blockchain, then its sheer size (>7 GB) may constitute a hardware constraint. But if you mine in a pool anyways, there is no reason for your miner to need access to the blockchain, unless you want it to verify that you do not unwittingly participate in a 50% attack.