I would do a one sided t-test.
You can obtain a one-sided CI as well, not a 2 sided, since you want to show one mean exceeds the other.
NOW, the next question, are you assuming equal variances, if so you need to pool the sample variances.
YOU can test to see if you have equal variances, via an F test.
The two t tests I am recommending are in...
Unequal sample sizes, equal variance
Unequal sample sizes, unequal variance
IGNORE the sample size comment.