For example, if my saas server goes down and impacts some customers and get myself sued...
for small teams, it seems to be difficult to fight these issues?
Do you own a side business? Are you concerned about this?
when you say limited liability company, does it mean only LLC? or C-corp and S-corp are also good?
The primary reason to form a C-corp is to facilitate outside investment by a particular class of outside investors. That class of investors includes traditional venture capital. There are few situations where forming a C-corp would provide advantages over an LLC: both are closely held, but an LLC is more flexible in terms of structuring controlling interests and payouts. That's why they are more popular.
My advice is to pay an attorney familiar with SAAS businesses for advice.
Good luck.