Welch's T test can control for uneven groups, and if you have large enough samples then central limit theorem applies so no need to worry if the original data i normal or not.
EDIT: sigh, you try to help people and get thumbed down for it. Central limit theorem isn't just some 'theory', it's one of the most fundamental theories in stats. It says that for any distribution with variance less than infinity, the distribution of sample means will be normally distributed. That's why you can use a T test on it, because a T test tests sample means against other sample means. The original distribution drops away. But CLT requires large samples to converge--larger for more non normal distributions, but usually only around 30+. The T test is robust with large sample sizes. But feel free to use other non parametric tests, but they tend to pay a price in power by having fewer assumptions. The other suggestion of the Mann Whitney U is fine if you want to go with that; I was just suggesting a simple familiar test.
