Here's a relatively short list of U.S. financial accounts that can be useful to a U.S. citizen married to a non-U.S. person and living in Singapore, along with a couple other ideas. I'll number these, but there's no ranking implied here. These accounts must typically be opened with U.S. mailing addresses, although in a few cases a non-U.S. address can be added later.
1. One or a couple U.S. credit cards with zero foreign transaction fee and (preferably) zero annual fee, along with supplemental credit cards for the trusted foreign spouse (you). If she doesn't have a U.S. credit history then the Capital One Journey Student Credit Card should still be available to her. Despite the word "Student" in its name, it's also available to non-students. U.S. credit cards really ought to be set up for full balance "AutoPay" from a U.S. bank or U.S. credit union account.
The value in a card like this is that it allows you and your spouse to spend at merchants that accept the major credit card without incurring foreign transaction fees. While there are some decent credit cards issued in Singapore, you're probably not going to beat even an average zero foreign transaction fee U.S. credit card.
2. A U.S. bank or U.S. credit union account. Lately I like Alliant Credit Union. She can open an account with them (checking and/or savings) then add you as a joint account holder. This account can support #1, and it also can help reduce or eliminate fees if you ever need to (legally) move U.S. dollars between brokers, for example. Or deposit a U.S. dollar paper check from the U.S. Alliant Credit Union issues a fantastic debit/ATM card linked to the account that has zero foreign transaction fee markup and that (get this) rebates fees that ATM operators charge.
3. A Schwab One account, also with their fabulous debit/ATM card linked to the brokerage account. (There is a Schwab Bank account she could also get, but that's less interesting and reportedly requires maintaining a U.S. mailing address on the account.) While this Schwab One account won't be for you, for her it's a pretty darn good choice -- for an IRA, notably. Beyond the brokerage account-linked debit/ATM card which works like that Alliant card, Schwab also has a pretty decent way to get funds into the account. Like Interactive Brokers, Schwab has a local account in Singapore where you can FAST or GIRO Singapore dollars which then pop up in your account, magically, as U.S. dollars. The conversion rate is decent.
4. Interactive Brokers. We all know about this one.
5. A TreasuryDirect account. She may or may not need this, but it doesn't hurt. This account allows her to buy U.S. Treasuries and U.S. Savings Bonds directly.
6. A couple official copies of her U.S. (I assume) birth certificate, one or both with apostille. Singapore isn't a Hague Convention (apostille) country, but the apostille can't hurt except for the minor fee involved to get it. An apostille helps making the document more widely accepted globally. If there are any other important civil records she wants to collect in the U.S., that'd be great. (For example, is she was married previously, prior marriage and divorce records.)
There is no U.S. marriage registry, by the way. If you and she get married here (in Singapore), there's nothing to do on the U.S. side in terms of filing any paper. A lot of people are surprised by that, but marriage is surprisingly relaxed in those terms. She just starts filing her U.S. tax returns as Married (not Single). And it's up to her whether she wants to change her name, but I'm not a fan if only because she then has to run around changing her name on accounts, her passport, licenses, etc., etc. I don't see the point, but of course it's her decision. Or you could change your name.
7. Voter registration, as mentioned. Then, while living in Singapore, every January she should send a new "FPCA" to re-register. (U.S. voters abroad need to re-register every year if they want to be on that year's voter rolls. U.S. federal elections are every 2 years, but I send mine every year since special elections to fill vacancies are possible.)
8. Any driver's license-related things she wants to do, legally of course. Caution on #7 and #8 that these acts might have state tax residency implications. If she happens to be staying in South Dakota, that's great, because South Dakota allows Americans living overseas to keep a South Dakota driver's license, or that's what I've read anyway.
9. If she wants to name a "Payable on Death" (PoD) beneficiary for any of her accounts, she can do that. Usually that can be done online, but in a few cases she might have to get a notarized statement or something like that.
10. If, post-COVID, she expects to travel a lot on business, and if she happens to be near the Canadian border, then she could look into getting a NEXUS card, one of the "trusted traveler" programs. NEXUS costs US$50, half the Global Entry program fee, and is slightly more useful because of Canadian entry privileges. Funny how that works. NEXUS card holders can then apply for an APEC Business Travel Card if they otherwise qualify. The U.S. variant of the APEC BTC isn't terrifically useful since it doesn't waive any visa requirements, but it does get you into the shorter immigration lines when you're traveling on business. Do we even remember what traveling is?
11. I haven't investigated this idea fully, but if there's a low monthly cost prepaid U.S. SIM card that'll roam in Singapore, to receive SMSes (text messages), that could be useful for online account maintenance and such. Along with a Google Voice phone number, for example. "More research needed."
12. A few "Forever" international first class U.S. postage stamps -- a book of 10, for example. They're occasionally useful if you have to mail something to the U.S. and include return postage on a self-addressed return envelope. The "Forever" ones mean that they're valid for whatever the rate class is, forever.
That's a pretty good list. Maybe Celtosaxon and others have some more good ideas.