A few starter questions for you:
Is the HDHP offered through your employer? If so, do they offer payroll deduction for HSA contributions? Also, do they offer any employer match?
If yes on payroll deduction, strongly consider this even if the HSA admin is less than ideal. Its hard to beat the immediate benefit of no payroll taxes.
If yes on employer match or contribution, make sure to get this free money. One thing to watch for is that employer contributions to an HSA, unlike those to a 401k/403b, do count against your annual contribution max.
If neither of these apply, you are basically an HSA admin free agent - free to chose any admin that works well for you. There are many HSA admins out there but you should be able to quickly narrow down the field to less than a handful. I would strongly recommend focusing on three things - fees, investment options, and investment requirements.
Fees - while HSAs are becoming more competitive, hefty fees do still exist with many admins. These include monthly fees, statement fees, etc. Now many are "waived" if your employer offers a plan with a specific admin - waived meaning your employer pays them on your behalf. Look for sub $2/month fees and an option for free statements via electronic delivery.
Investment Options - good news here is that many admins have recently seen the light on low cost index funds via Vanguard, Schwab, Fidelity, etc. If an admin has none of these, strike them from your evaluation list. Now you don't need that many low cost index funds so don't be alarmed if an admin has say 4-5 index funds and many costly other funds. A few admins give you access to low cost investing via commissionless ETFs which are essentially low cost index funds that have been made to trade real time like a stock (read up on this if you are truly interested in learning. It is not as scary as it may sound).
Investment Requirements - many HSA admins have hurdles to cross before you can invest. These hurdles are often dollar amount based like "you can invest any amount after you reach $3,000 in your HSA savings account". So your first $3k earns near zero rates and then you get to invest the rest. For someone who wants to invest all of their money, this is a frustrating hurdle. Look for admins that allow first dollar investing or at the very least a very low hurdle before you can invest. Good news here is that first dollar investing is becoming more of the norm but not all admins have yet to admit the market is demanding this.
So who should you consider? Here is a short list of HSA admins that are some of the biggest yet also innovative. It is not an exhaustive list and definitely doesn't include any smaller providers like the growing number of credit unions getting into the HSA world.
The HSA admin your employer has partnered with
HealthSavings - you mention this admin already
HealthEquity
HSA Bank
WageWorks
Optum
Good luck with your HSA setup and let us know how it goes.