It really depends on the level of service and type of relationship that you will need.
Basic - deposits, check writing, etc. - all done online. You can shop for the best fees and user interface.
Need financing (loan) in the future - it's important to establish a personal relationship. Note: typical AR (accounts receivable) financing is not available for SaaS companies. In the typical AR situation, a company has delivered the product/service and has billed the customer. The bank essentially "time shifts" funds by loaning against the outstanding receivables and gets paid when the customer pays (sometimes directly). In a SaaS model, even though you may have long term contracts, you are paid upfront (perhaps monthly) and then you deliver the service. There are no receivables to finance.
Still, some alternative lenders have figured out how to financing SaaS contracts. Sand Hill Finance was one (now part of Square One Bank).
At the next level is the possibility of venture debt. Then, you want a relationship with a bank that has a venture/startup department. Silicon Valley Bank, Square One Bank, Bridge Bank are the big three (and I see that City National Bank is active in venture financing). This list undoubtedly is incomplete. Note: venture debt generally is issued based on the VC's relationship with the bank, not yours. But it doesn't hurt to have a pre-established banking relationship.
I've just hit the surface, but hope this helps.