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Your biggest problem is going to be the 4 GB of RAM. Saving a few hundred megs on the DE will help but not much. If you run a web browser ( and I cannot imagine using a computer without one ) that RAM is going to fill up fast.
Honestly, I would use a 32 bit distro on that hardware.
Q4OS with Trinity, Antix, Adelie, and DSL are all pretty decent options.
I used a system with 6 GB daily until not long ago. I had to constantly restart my web browsers to reclaim memory. RAM was a constant issue. A 32 bit distro made things a lot better.