Definitely do not use 1xbit - they have a really bad reputation on the forums for a reason.

I have used Loot.bet and Buff.bet quite extensively and never had any problems. Their limits are pretty reasonable in the esports sphere, but obviously don't go out there and expect to be able to bet tens of BTCs at a single time - that is just not realistic.

Also check out some of the esports books that use skins/in game currency as units of account, they might have larger limits.