BOA and Chase seem to be the most generous with starting limits for many. Citi starts out more conservative. Amex also may start out with lower limits, but in a short time you can easily make it a higher limit with just soft pulls. BOA and Chase are also very easy to get a high limit with combining limits since you can reallocated limits at any time. My first BOA card was opened in 2014 and has a $50K limit now.
Many credit unions are more generous with starting limits such as PenFed, UNFCU and NFCU. My NFCU limit is up to $50K now as well.