We use a large 600x900 high power Chinese laser for commercial purposes - luckily enough I am allowed to use it for model boats .
With lasers its not worth buying a small one - or one too low powered. The open frame ones coming from China now are mostly underpowered and very dangerous . There is no provision to remove the smoke emitted when cutting - smoke alone can damage your lungs never mind the fact that a lot of it is toxic & highly dangerous - even MDF contains formaldehyde which is pretty nasty stuff . The minimal safety provisions on the the open frame ones are to say the least laughable .
Minimum useful bed size is around 500 - preferably 600 - ( usually 600x 400 nominal - IE about 560x360 ). Minimum power 50/60w - preferably a honeycomb cutting bed - best beds are movable to allow deep objects to be cut or engraved - and lastly it MUST BE fully enclosed . There are a lot of nasty emissions from high powered lasers - its not just your eyes at risk.
A separate cooler is required for the laser tube - and a good smoke extraction unit - in the UK I believe you would need to have an emissions filter system to remove the pollutants.
Dodgy who used to be on this forum bought an open framed CNC router - its only really strong enough for balsa which was his main requirement - it generates a lot of dust ! - he was considering a laser attachment but looking at the risks decided against it.
There are some desk top models available which might be suitable - but they have a lot of limitations like limited usage time before requiring a rest period - plus they cost very nearly as much as a full scale one and you still need the anti pollution unit etc which itself is expensive.
There is a long list of items that should not be cut on a laser - learnt the hard way vinyl is one of them - emits a very corrosive toxic gas . See the PDF attached !!!
All in all unless you have an ongoing use for the laser it would be better to outsource the cutting as the cheap ones can be lethal in many ways - (bear in mind even a 30w laser can easily cut a finger clean off ) and the good ones make an expensive toy !