Welcome to the forum!
First, is your 4G hotspot a MiFi? If it is USB, it most likely will not work due to lack of drivers.
Secondly, do you have a computer at home that you can run Google Chrome browser on? If yes, you can use ANY printer and set it up through Google's Cloud Print (in the settings of Chrome).
If you can use Cloud Print, you can then get the Cloud Print app for your TF300 and then print from anywhere you have internet. It will be waiting when you get home so long as your computer at home is turned on.
If you are going to get a new printer, getting one that is Cloud Ready (Specifically for Google Cloud Printing) and you can use that to print.