It really depends on what's in the tank. Will you have one or two turtles in there? Make sure the filter is the right size. For a 40 gallon tank and a single turtle, you want a filter rated for 120 gallons or more. People usually go by the 3x (tank size) rule, but others like to do 5x. A filter is a good investment as it cuts down how often you need to do complete water changes. That tank is a lot better than what you have Turquoise in currently. If your mom is really worried about salmonella, then keep some germ-x or other antibacterial handy for whenever you handle the turtles and their accessories. I've been caring for my turtle since I was 7, so your age isn't an issue.
Edit: As for it being, "impossible" for you to clean the tank on your own, it really isn't. I used to use the bailing method for water changes. It's a lot of work, but it's possible. You might want to look into getting a python water changer. I've got the Aqueon version and the handy thing saves me so much time and effort. I don't have to move my tanks or many many containers of water any more thanks to it.

RES: Turtley - about 9" (She makes it a mission to measure her. :/)
Musk: Bolt - 4.5"
Mutt: Gaviota - small