Damon - photo paper for a home inkjet can closely resemble lab photo paper, even if the process is different. It can have decent weight and come in gloss, matt, etc.
For smallish prints another option is something like a Canon Selphy (less desk-space).
Arguments against home printers are that they take up space, are often short-lived, can be cantankerous both mechanically and software-relatedly, and tend to be expensive in consumables as well as being time-consuming to operate. Also there's an environmental aspect, that a printer in the home is yet another short-lived consumer 'durable' to add to the river of other items that our homes are often stuffed with and which are on a one-way trip from raw materials to landfill having used up energy on the way. The popular ethos seems to be that if you can afford it, then you have a right to have it, but the poor planet's groaning under the load we're putting on it. It's not just about us, now, it's about our great great great grandchildren ...
As an alternative, photo files uploaded to a lab service are cheap, and often arrive in the post the next day. There might be a small learning curve in preparing files for print, but you get that anyway.