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So I found some Khorne Daemons for cheap (5 dollars below regular price, and 25% off that price additionally, so it was a steal), and i'm wondering if I have to absolutely swap them to circular bases? I'm not quite sure what the ruling is on it. And if so, what size for a Khorne Bloodletter?

It is not necessary but it is considered good manners as it helps your army to look uniform as well as keeping measuring more consistent as a square base is not the same size in all directions. For example if I declare a charge with a model with a square base and I have the corner pointed at the enemy and am measuring from that corner I will actually be a little closer and could make say a 8" charge become a 7" charge that I would not get from a round base.
For Bloodletters I would use the official 32mm.
Here is an article to help: http://www.belloflostsouls.net/2015/08/tutorial-rebasing-your-fantasy-models.html
and a video:

It's completely optional, but re-basing minis is pretty darn simple if you want to match them to your army.

Its not necessary to do this. But they look cooler if you give them 32 mm bases.
Recently, I have rebased my whole BA infantry from 25 mm to 32 mm. Big effort but it was worth it.

My 40k DP is on a square base.

Those sharp corners are so metal.