You can reimburse yourself for qualified medical expenses after the HSA is established, which is generally the date the first deposit was made to the HSA. Note that in the case of a married couple, these dates very well might be different.
If you're married, you can distribute from your HSA for your spouse's medical expenses and vice-versa.
Prescriptions and copays count. Also, as of the CARES act, over-the-counter medicines count. Menstrual care products also count.
The age for penalty-free withdrawals for HSAs is 65. This is different from IRAs, which is 59.5.
I keep a single Excel spreadsheet with date, amount, brief description. I keep paper receipts in a hanging file folder in my filing cabinet.
It sounds like you are, OP, but make sure you are reporting your contributions on your tax return on Form 8889 and Schedule 1 line 13. Distributions are also reported on Form 8889 in the year taken.
I would add to
@EvenSteven's comment in their second paragraph a bit - that is only true if you weren't going to max out your other tax-deferred savings options otherwise. It is somewhat better from a wealth building perspective to max out tax-deferred savings *and* keep the money in the HSA (as OP notes, it's a tax-deferred vehicle as well) if you can because you're tax-deferring more money in total. The point about simplicity and receipts is still true.
Finally, note that HSAs are not taxed very kindly if a person dies with an HSA. For this reason, I plan to drain my HSA by some time in my 70s.
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@BC_Goldman, you may want to switch HSA custodian, or you might not actually have an HSA account. The HSA custodian is under no obligation to require receipts for a distribution - the burden is on the taxpayer to prove a distribution is qualified. While I haven't made a distribution from my HSA yet, my understanding is that Fidelity (my HSA custodian) doesn't require receipts.