HSAs are pretty attractive options. Unlike a Roth, your HSA contributions will reduce your AGI (and your taxes!). Some HSA providers are fairly low cost, and have good passive investment options (HSAdminstrators, for one). Any contributions grow tax-deferred, and can be withdrawn at at time tax free for qualified medical expenses. Plus, you can take out the money at retirement for any purpose, although the withdrawals are taxable (like a traditional IRA). Unlike an IRA, there are no required minimum distributions on HSAs, so the money can potentially grow tax free for the next 50 years. Many bogleheads utilize HSAs for retirement savings rather than their intended purpose of health savings accounts because the tax benefits are just too good to pass up: the money you invest isn't taxed, it grows tax free, and is tax free at any time for qualified medical expenses. That is as good as it gets from a tax standpoint.
You are relatively healthy and have a long and lucrative career ahead of you. I think many bogleheads would advise you to self-insure as much as possible (i.e., carry insurance with a high premium). I max out my HSA and carry health insurance with a $2k deductible. My monthly premiums are considerably lower than they'd be with a lower deductible, and the difference funds my HSA. Many bogleheads (myself included) pay their medical expenses out of pocket rather than through their HSAs because the tax benefits of leaving the money where it is are so attractive. But it is nice to know that, in a pinch, the money is there for a true medical emergency.
I think your second option is the better option: I'd split the $5000/year between a HSA and a Roth (I'm assuming that as a resident, your current tax rate is substantially lower than it will be in the future).
So I am a recent graduate of medical school and will be starting my residency in California. I made a budget for myself and figured I can put in roughly 5000 dollars of investments each year. As my employer doesn't offer a 401k match, I was thinking of either funding a Roth IRA fully or funding an HSA and part of a ROTH IRA.
The only reservation I have is in order to be eligible for an HSA I would have to pick a health insurance with a 1700 deductible as opposed to one with no deductible. Im a relatively healthy 26 year old and dont envision meeting that deductible so that would be my reservation. Also the fact that I will be in California and that an HSA wont help with my state taxes.