Play would tend to indicate an issue with your bottom bracket bearings, not the crankset. If you have a cartridge bottom bracket, it needs replacing if it's got play. If you have a cup-and-cone one, you can disassemble, service and adjust it so it runs with no play. Your crankset is probably fine.

If you do replace the crankset, there's nothing to say you need the same number of teeth on the chainring - if you have fewer teeth, you'll get a lower gear, but you'll probably have to shorten your chain. If you have more teeth, you'll get a higher gear, but you'll probably need a new chain, as your current chain won't be long enough.

If you get a crankset with different-length arms, you'll have to adjust your saddle height, but nothing else should change. Technically longer cranks give a slightly lower gear, and shorter ones a slightly higher one, but the effect is minimal.

The main issue with replacing a crankset is chainline - how far out the chainring is from the centreline of the bike. If you don't match the chainline, your chain will run noisily, or it won't stay on. Different cranksets will have different chainlines with the same bottom bracket spindle.