Since you don't know what switch you want (which is extremely important actually), do not buy a $350 keyboard.
Buy a cheap board with Kailh hot swaps (not Outemu or pretty much anything else). I kind of like the GMMK but they don't make a 65%, Keychron has one due to release any day, both are, or should be around $60 USD or so. With this you can order switches and pop them in.
Why cheap?
Hotswap offers more switch options and the ability to play but there are some serious downsides. Hot swap limits layout options so that could be an issue for you, but if it's just to find your switch it may be worth it to use short term before buying a nice board. On some cheaper keyboards, the switches are a huge cost of a keyboard and you can sometimes just about get the board free so why not, if it's a mainstream switch take the opportunity to try a new layout and keep it as a spare board. Only once you zero in on your preferred switch, THEN go all out on a nice board but you really need to figure out what you want from a switch beforehand as there is just so many options these days. Many of also us don't like recommending hot swap for long term use as it's just another fail point, great for playing though, so my advice is go cheap here then decide for yourself before you buy a nice board.
Speaking of, most nice boards are not hot swap, this is changing to a degree but I'm not sure it will become the norm any time soon for the reasons I mentioned, at least for now, the hobby needs time to sort out if it's the right way to go or not and you need to sort out what you need as well. Maybe by the time you find your switch the right board will also be waiting.
That $350 limit kind of puts you in an odd place, more than enough for a nice board like a Ducky but not enough for something really exotic. That doesn't mean zero options, just limited. You will probably be looking at a Chinese kit from somewhere like KBDfans or Krepublic, which is not bad thing at all. A bonus here is you can buy extra plates and PCBs pretty easily in case of a problem or just wanting a different switch. The only downside is ship times from China are SLOOOOOW right now. I do believe some airmail is shipping now but they are still really backed up on manufacturing, orders and shipping. There are a few other options but 65% only recently really seems to have caught on so options are a bit limited, it will be months before every manufacturer has an offering.