Looks like a kohler mixing valve. Call kohler and talk with tech support. You can submit a pic if that valve and they will let u know your options for trim More on reddit.com

It’s generally a good idea to take the local plumber’s advice on brand, as he is more familiar with what’s used in your area. For example, all these guys are saying Moen, but we aren’t a big Moen territory where I live. Most plumbers know Delta and Kohler. If you buy Kohler, you need to buy an 8304-KS-NA. This is the valve that 90% of their shower trims are made to fit on and it has stops (which allow it to be serviced without turning water off to your home). This one has sweat/threaded connections that allow the plumber to use any piping system on it. 8304 trims have one handle that goes left and right to control volume and temperature at the same time. If you get Delta, buy an R10000-UNWS. This is Delta’s universal shower valve, it works with all of Delta’s shower trims, most of Peerless’ shower trims (Delta’s builder grade brand) and most of Brizo’s trims (Delta’s higher end, showroom brand). Delta has three trim types: T14, T17, T17T. The T14 has one handle that goes left and right, and controls temperature and volume together. Both the T17 and T17T have two stacked handles that turn left and right, the smaller one in front controls the temperature while the larger one in back controls volume. The T17T is the same function but with a different type of cartridge that allows for a higher flow rate. If you get Moen, you have two options, Posi-Temp and M-Core. Posi-Temp: Get 2590 valve (threaded connections that can be adapted to any pipe, with stops) Posi-Temp trim has a single handle that controls volume and temperature together by going left and right. This valve will work with any Posi-Temp trim. M-Core: Get the U140CIS valve (copper sweat/threaded connections that can be used with any pipe, with stops). M-Core has three trim types like Delta does, the 2-Series, 3-Series, and 4-Series. The 2-Series is like the Posi-Temp, Delta T14 series, and Kohler, it has one handle that goes left and right to control volume and temperature at the same time. The 3-Series has one handle that pulls out to control volume and goes left and right to control temperature. The 4-Series is like the Delta T17T series, it has the same type of higher flow cartridge and uses two handles, one small to control temperature and on large to control volume. This valve will work with any Moen 2,3, or 4 series trim. My suggestion is to find a plumbing supply house/showroom local to you and tell them that you need to buy a valve, and explain your situation. They’ll know what local plumbers prefer and help you make a selection. Hope this dissertation helps. More on reddit.com

Hansgrohe ❤️ ❤️ But seriously since you don’t anticipate staying for long, put whatever you want in. It’s doesn’t matter as much as how well-installed it is. More on reddit.com

I think you can have pex going into the supply of the valve, but you are supposed to use copper between the valve and shower/faucet. Read the instructions for the valve. The last one I bought said copper only between the valve and faucet. If there's any warranty you'll probably lose it if improperly installed More on reddit.com