do what you have to for the mean time, but then save and build a suitable permanent home as you can. The turtle will do fine for a few weeks or month in a tub with a rock and a desk lamp for light if that's what you need to do.
As a fish person, you should be ready to handle this, but there is one big thing you need to learn. Turtles bring about ten times the bioload of fish per size.
Normally folks say take one inch of fish per gallon of water to make an easily sustainable tank.
Make that 10 gallons per inch of turtle. I would encourage you to make sure you know the sex of the turtle (if it's little and you can't tell, guess female) find the adult size of that particular subspecies in inches (carapace length) and then multiply by ten. Set up a tank that has that many gallons OF WATER. Remember, in a turtle tank you drop the water level enough so you can put in a basking spot and still have the lid on it, or else you need to build an external basking spot. So for instance, you can put 30 gallons into a 40 breeder, so it would be good for a 3 inch turtle.
For a painted, if the subspecies had the adult female size of say 7 inches, you'd want 70 gallons of water and enough air space above that to have your basking spot, so something like a 90 gallon would work nicely. Larger is ALWAYS better, even for hatchlings.
For filtration, I HIGHLY recommend using a UGF filter with a THICK layer of gravel on bottom of the tank. You can put large river stones over that if you are nervous about the eating of gravel, but I tend not to sweat that much (though you should be aware that very very rarely, an animal can get sick or die from eating gravel, but it is very very rare for them to get sick and even more rare for them to die from this). I would use normal powerhead setup for this (except drop your intake hoses down enough that the powerheads are working right in the lower water level, obviously) like you would for fish.
Now, I would ALSO have a cannister filter like the fluval 404 or the xp3 or whichever you like. Why? Because it will suck out most of the junk and "polish" your water nicely, while your UGF works as a great bio filter cleaning out fine junk and chemically handling the ammonia... I used this for my winter tank this year and I didn't have to change water all winter, just add more and do one partial change and two filter cleanings.
it was wonderful. And I had way too much turtle for the tank (it was a winter quickie job, they live outdoors normally, which is the best life at turtle can have).
Good luck.
Oh, and for a painted, don't bother buying a heater. You don't need it if this tank is in your house, unless you keep your house below the mid 60's.