If you are purely out to learn, consider mining on the bitcoin testnet (the alternate bitcoin network that is identical except for running on a different port and allowing non-standard transactions). 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.
