A ten gallon is a good home :) Turn the filter on low, if not an option use an aquarium sponge (cut as needed) to place in the outflow section to soften the current (a new/clean rubber band should hold it into place if needed).
A heater is also very welcomed for them. I personally order mine from here
.. a 50 - 100 watt should be enough. They all are thermostat where you can set the temp to your liking. I use them for my 1.75 gallons up to my 30g+ grow out tanks for the babies and even the tubs that are set up to house the juvies. Have yet to have issues with any of them (I have both types of the minis, along with the 100w and 150w ones). The prices for them there are a good price and delivery is pretty quick. If you have your own heater, then ignore all I wrote :)
A 10 gallon can house a few friends if you do wish to add down the road - sometimes it's hard to have just one betta, so you can purchase or make your own dividers and have 3-4 bettas in there, or you can add 3+ cories, or other peaceful fish such as platties/swordtails. I recommend staying away from the barbs and some of the tetras as they can be agitators and fin nippers. Or you can have him by himself if you wish. Some bettas may become lonely if left alone or not in a part of the house that tends to have a lot of activity, so keep that in mind in case you question his "mood".
As long as there are plenty of plants and a cave for him to sleep in, he should be happy :) I also recommend this site for buying plants that are soft (along with anything else.. the betta hammock is a few dollars cheaper here than anywhere else). I purchase from here
and am extremely happy with what I get and it usually arrives in less than a week of purchase.
Don't forget the conditioner! And water change recommendations for your size tank you can find here
I wish you luck with Junior and his new home :) And don't worry, everyone has made mistakes when it comes to learning about caring for these guys.. too many myths out there! Looking forward to pictures!