Among triathletes, "the best" wheels are widely considered to be: Zipp, Enve, Reynolds, Mavic, HED, ... Zipp is about 6x more common than the second most popular wheel maker, Enve. (Source)

Some of this is because of sponsorship, available discounts, etc.

A typical pair of Zipp or Enve wheels is going to cost $2,500 or so.

I wouldn't trust used carbon rims unless I knew their history and how they've been taken care of. I like my teeth. Anyway, there's a thread in the road forum right now where people are debating whether $1,250 for a used set of Zipp 303 wheels is a good deal or not.

I'm sorry to be the bearer of bad news but you aren't going to get "the best" wheels for your budget. You probably won't get better wheels than you already have for $300, unless you buy the parts and build them yourself. But it depends how you define "better." You can still buy wheels and maybe you'll prefer them, but they'll be more of a sidegrade than an upgrade.

If you're a new cyclist there are probably a lot of other things you could spend the money on that will do more to improve your time on the bike.