What’s an inexpensive way to finish out our upstairs bonus room ?

I have a mini split air conditioning wall unit. I agree that it is somewhat unsightly but it is worth every penny when it's so hot you can't breathe. It also adds heat in the winter. It was far less expensive than central air. You other option is a window unit but I happen to like my split system much better because I don't have to take the window unit in and out winter/summer. It's just there, I turn it on and off, and don't give it a second thought. If you can do a lot of work yourself finishing the walls, ceilings, and floors in this area you can save some money. Shop for the best bargains and buy things on sale and if you can find some reclaimed goods you can use that are a reasonable price--go for it. I agree that remodeling can get expensive but if you want an art studio space you have to lay out some cash. It will also add some value to your home and give you a new space to spread out. You will wonder why it took you so long to do it!

I saw an internal heating and cooling unit at Costco a month ago. It was quite nice and not that expensive.

We have a portable air conditioner/heater that works great that would work here too. But your biggest challenge will be putting insulation and dry wall up in the space to make walls.

As you have read, installing a split unit will eliminate costly ductwork installation. When the mess is cleaned up from the ac unit, I recommend painting the walls and trim so as not to despoil the newly installed carpet. Good luck in your endeavors.

Can you have ceiling fans installed? They will have keep the air up there circulated and they are a good way to get relief when its hot and humid. What kind of artist are you? What I mean is what medium do you use to create? It can make a difference in what pieces you put up there for storage and if you paint you'll want a way to ventilate.

I too am an artist but I mainly use colored pencils and at the present my studio is in a small room on the main floor. So what ever way you decide on keeping your studio cool or warm make sure you also have ventilation if you paint.