If you get the Antec 300 Illusion, it comes with fans pre-installed. I haven't looked at the "regular" 300, but it should come with fans too. It's always a good idea to improve airflow throughout the computer case. Just remember, not all air flow is ideal. If you get too much air from the intake, and not enough exhaust to pull all that out, you're circulating warm air, not cool fresh air.
As for other options, an after market CPU cooler would go great with a new case. That may put your budget a little overboard though, so saving up may be inevitable.
As for the case, the Antec 300 is a great case, and very well recommended here on T-F. I personally like the Xigmatec Midgard-W, it has a little more features than the 300, and can hold up to 7 cooling fans (2 are preinstalled).
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