Compatibility of 38T chainrings to Deore crank
There is no difference between a Shimano 11-speed 1x chainring and a 10-speed one. There is a slightly difference in the OUTER ring(s) of a 2x or 3x chainset, because 11-speed chains are slightly narrower and this affects shifting from smaller to larger. However single speed rings are completely identical between 10 &amp; 11 speed, so you don't need to worry about 1x '11' per se.
A 1x drivetrain is quite simple upfront with much less to go wrong in terms of poor shifting performance etc. Normally you'd have to worry about derailleur capacity etc. but with only one chainring that's not an issue.
The only considerations might be:

material - some materials will be lighter, which is not a major concern at this size, others might be more durable e.g. hardened steel
narrow/wide - this is a good idea for chain retention on 1x drivetrains
BCD &amp; bolt pattern - you have noted this already
price - if you buy something very expensive you could end up spending more than a new chainset, where your current one is a simple one with solid arms, whereas more expensive models have hollow (lighter, possibly stiffer) arms. So you don't probably want something too complicated