I don’t mean to harp on this, but are you absolutely sure you’re on an HDHP? It’s not enough to have a “deductible that is high;” there are also a myriad of other conditions, like HDHPs do not pay for prescriptions until the deductible is met, there is a proscribed out-of-pocket maximum, etc. Look for specific phrases like “this plan is HSA eligible”.
I ask this again because it is unusual for an employer to offer an HDHP with a FSA and not an HSA. You should also check to see if your FSA is a general medical or limited use plan. A limited FSA plan is for things that aren’t typically covered by medical insurance, like dental, vision, or dependent care. If you know the FSA is a limited plan, then you could in fact contribute to an HSA as well.
See
https://thefinancebuff.com/hsa-and-fsa-same-year.htmlNow assuming all of this checks out, shopping for an HSA is basically like shopping for a bank. Here are some general questions you might ask. Prioritize based on what is most important to you.
Are you FDIC insured? (This is a must for the non-investment portion IMO.)
What is the regular interest rate in the checking account?
What are the monthly fees?
What are your other fees?
Is there a minimum holding amount that would allow me to waive fees?
Do you link directly to an investment house?
What investments are available to me?
What are the monthly investment fees and minimums?
Do you have a local branch? (I don’t think this is typical but maybe that’s important to you.)
Do you offer useful, complimentary features, like 24 hour customer support, record uploading, how-to guides, etc?