I have a gas line in the house already so I thought it might be a better fit and cheaper to get a gas one, but not sure how much it cost to have an electric stove installed compared to a gas one.
Are there any things I should know about if I want to place a cooking stove in the basement?

The installation cost would be about the same. Having said that, there are a few variables. If you go with gas, you will need to have it vented to the outside. If you have a way to vent it, the gas is probably going to be cheaper to operate. There are some ventless gas heaters on the market, but I would not trust them in a tight space such as a basement. If you do not have a way to vent the gas, you will have to go with the electric. We recently needed to add heat to a similar space, and bought an electric fireplace, which has a heater built into it. Works like charm, and we have the added beauty of the fireplace. (New ones look very real). Good luck.