It's all a bit of a minefield - you've got competing, incompatible rules in each country (MiFiD/PRIIPs, PFIC, HMRC reporting, FATCA, etc.). But there are reasonable paths through it, without doing too much paperwork or paying extra taxes! Although I will warn that there are plenty of grey areas where even the experts don't agree (and I'm just an educated amateur
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First stop would be a UK pension - workplace pension if you have it, SIPP if not (some grey area on the SIPP, but pretty confident it's ok). At the very least up to the employer match (free money!), but also as a primary investment vehicle for retirement. Tax advantaged in both countries, no PFIC issues so you can buy whatever funds are offered by your provider, it's ideal. Finding a UK broker who will open a SIPP for a US citizen can be a challenge; I know Hargreaves Lansdown will, there are likely a couple others, but not most (thank FATCA).
My second preference is a US Roth IRA. Also tax advantaged in both countries, no PFIC issues either. MiFiD/PRIIPs can get in the way of buying US funds, so you may wind up having a US IRA but buying UCITS funds in it. Typically this would be a big red flashing PFIC warning, but the IRA wrapper means it doesn't matter. Probably only Interactive Brokers will allow you to open an IRA using a UK address AND buy non-US funds inside it, but it's all above board.
After that, many people would look to a UK Stocks & Shares ISA - but BIG PFIC WARNING applies here. The US DOES NOT recognize the ISA as a tax-advantaged account - to the IRS, it's just a taxable brokerage account, and any non-US funds you buy in an ISA will be taxed as a PFIC, with punitive tax rates and extremely onerous filing requirements. Unless you really know what you're getting yourself into, DO NOT BUY A FUND IN AN ISA. Individual stocks are fine, if you're comfortable managing them, filing US taxes on dividends and capital gains, etc. Same challenges on finding a broker, too: Hargreaves Lansdown and Interactive Brokers definitely work with US citizens, likely a few others out there. Cash ISA is fine, but interest is US-taxable and usually worse than a savings account - unless you have a LOT of interest, you're better off with the highest rate savings account you can find.
Stocks & Shares LISA is the same concern as an ISA. The UK government 25% top-up is nice, although US taxable. Cash LISA is fine for saving for a house; wouldn't want to leave long-term investments in cash like that.
That pretty much leaves taxable brokerage accounts, either in the US or UK. Same tax rules apply regardless of where the account is open - avoid PFICs! If you can use a US address to open one, it may make it simpler to buy US funds (non-PFIC), and you'd want to pick HMRC reporting funds (
https://www.bogleheads.org/wiki/Vanguard_US_domiciled_ETFs_that_are_UK_HMRC_reporting_funds) to avoid punitive UK tax. If you use a UK account, or even a US account but with UK address, you'll likely be barred from buying US funds, and you don't want non-US PFIC funds, so you're stuck with individual stocks. Or you can get a bit exotic by buying and exercising options to get the underlying.
That high-level summary ignores some of the more exotic options like HSA, 529, VCT, EIS, SEIS, IF ISAs, etc., but you likely don't want to mess with any of those. And there are plenty of nuances with all of these options - I urge you to do your research before investing, but hopefully this is a starting point