Like u/stowgood alluded to, a dye-sub printer is absolutely the way to go here and in range budget wise...

Pros:

• Longer Warranties(some 5 years)
• Support
• Simple(hardware/software)
• Robust
• Repairable
• Faster
• Better Quality(color)
• Form Factor
• Tried and true(commercial/residential)
• Travel well
• Workhorses
• Withstand environmental changes
• Set it and forget it
• Low maintenance
• Straightforward(easy to compare models)

Cons:

• Limited features
• Limited page sizes(kind of)
• Limited media(kind of)
• One trick pony
• Upfront cost

You'll find them in labs, photo booths, kiosks, retail establishments etc. and made to take a beating. In a residential setting, should last a long time.

Just get one, it's your only option before making a very large investment or getting them printed by a 3rd party. They're basic and featureless which is what you want in a BIFL scenario(less crap to go wrong). No consumer grade inkjet or laser printer can touch them within your budget.

Great machines.

Ignore the Brother's, Selphys and Printoss's in this list(sort high to low and work down):

https://www.bhphotovideo.com/c/buy/Dye-Sub-Thermal-Printers/ci/1108