At least it's a RES turtle. It's one of the hardiest to start with so you have some time to get things together. Lighting is very important , you must have "both" UV (UVA) and UVB , for the health of a turtle. Both needs to be over the basking area ! The UVA (heat) is to entice the turtle to get out the water and the UVB which is a specialty bulb provides the proper rays for health. UVB does not produce adequate heat alone unless you get into the mercury vapor type. But those are not meant for a small tank ! Maybe 90 gallons and up !
Here's an idea of what's needed :
Item (for a 40 gallon indoor setup) Basic Premium
40 gallon tank Rubbermaid container* $15 Glass aquarium (Long) $60
Submersible water heater 100 Watt heater $18 200 Watt heater $20
Water filter Aquaclear 110 $45 Rena FilStar XP3 $120
( 5% ) Compact Flourescent $23 ActiveHeat MVB $45
Heat lamp (For basking) Incandescent bulb* $1 --MVB produces heat--
Thermometers Various, brands $2 ea. (2X) Temp Gun $25 ea.
Basking area/platform** Zoo Med Turtle dock $22 Acrylic Turtle Ramp $35
Lamp fixture/reflector Generic* $5 (2 required) Exo-Terra Glo $16
* $138 (estimate, U.S. funds) $321 (estimate, U.S. funds)
Note: It is advisable to invest in larger and better equipment to reduce the frequency of incremental upgrades. Costs for netting, food, treats and decorations are not factored into this chart.
Take the time to do a lot of reading it will help to have a happy , healthy , long lived turtle. Just remember the smaller and cheaper you go now will be much more work for you. (maintenance)
The 10 gallons of water for every inch of shell is not just for more swimming room But for you to be able to control the waters parameters for a cycled tank which will help you keep tank clean so your filter can do it's job. Filters are sold as fish gallons and turtles are messy so need 2-5x's the flow of fish : a baby needs 2x's flow of fish , juveniles need 3-4x's flow and adults 4-5x's flow with the needed amount of water to maintain a cycle. Also a filter that has mechanical , chemical and biological media is best for a turtle. The larger media area the better. Much info out there on cycling here's just one : https://aquariuminfo.org/cycling.html
Media that comes with filters are mostly for fish adjust for a turtle read here : viewtopic.php?f=9&t=30145
Turtle's get big and live a long time , the initial start up cost can be a lot. Males can get 9" depending on it's DNA needing 90 gallons water alone. Female's 12" needing even a larger setup. A glass tank for an adult alone can run several hundred dollars , myself on a retied man's budget so I use stock tanks 1/4th the cost and last forever. Shop around and use a price tracker for best pricing. Farm supplies stores and tractor supplies are best to look at , nursery’s and big box stores are over priced ! Those are thin plastic too , a farm supply store uses much stronger material like in the Rubbermaid ones. They are wider than glass tank’s offering much more room to do things and the outside only limited by ones creativity to make them look great. I use the saved money for a good filter.
Example : Today a 4" turtle would need 40 gallon tank full of water with an "ATBA" ( not a 40 gal half full ) but even that has no room to grow. If you can't build a "ATBA" you could get a 90 gallon tank fill half way and place basking area in tank so it can't escape. Then as it grows fill all the way with an "ATBA" . That will buy you some time until another upgrade is needed depending on it’s growth and DNA for full adult stage ! Or if you can swing it just setup an adult size tank and save on all those upgrades. Then trying to sell all those small tanks / filters you have in storage.
Small water volumes are almost impossible for some to achieve a cycled tank , the large water volume's can hold a cycle easier which is you best friend on a cleaner tank so a proper sized filter can do it's job. This will make maintenance much easier ! See some of my videos on my water , I believe my setup has clean / healthy water and is matched / balanced for it's size . This is achieved with weekly water changes ( no way out of water changes) and with my setup I only have to clean filter once a month using above method.
Most think changing larger water volumes will clear up a tank but that Kills all your good bacteria needed for a cycle. Never do 50% or larger water changes unless a health problem. One must find correct % for “there” tank being all setups are just a little different. 10-20% water changes are much better , not killing off your good bacteria along with proper filter maintenance. With your bio media never use tap water to clean that will kill you good bacteria only use tank water to rinse it off. That brownish junk on bio rings is your good bacteria do not try and scrub it off only rinse with tank water.
Being an old timer I do not use "any" chemicals for my water but I use carbon to remove any toxins. Most long time turtle keepers try to keep chemicals out our tanks so we have control !