You can get by very cheaply if you just want to engrave small wooden pieces. You don't need anything fancy at all.
My first laser was an Ortur laser master 2, and you can have it if you want it because it's just laying in a closet in 'ran when last hooked up' condition. On the other hand you can get something similarly useful for your use case for probably a hundred and fifty bucks new.
Be aware that claims of power and wattage on inexpensive lasers are almost always lies. My LM2 says it's 20 watts- in reality, it's probably 5-6. Take Chinese ad print with several grains of salt, although some do have real power.
That said the power is almost unimportant if you don't actually plan to cut with it, and diode lasers are overall pretty poor at cutting. For engraving you need very little power.
I haven't hooked it up in forever (I have newer and better) but here are some projects it did. These cheaper machines do need to remain hooked up to a computer- i used a $60 ebay refurbished laptop for it. Works perfectly fine. Lightburn is the undisputed king of laser software and it is inexpensive and one time purchase.
Honestly? Fun to play with, easy to get into, and i've spent more on single hand planes. Worth jumping into.