Yes, you do need gloves to protect your hands.
You absolutely do not have to go clipless right now - or ever if that is what you want! Do not allow anyone to tell you that you aren't a real cyclist if you do not clip in - I have actually had someone tell me this. It is your ride and you need to do what works for you. I ride quite long distances with BMX pedals - so far the furthest I've gone is 70 miles without clipping in. I've had foot surgery myself so I understand.
If you do decide to stick with platform pedals, you should probably look into better pedals than what came with your bike eventually. Personally I prefer BMX pedals because there are pins that give my shoes something to grip and my feet stay where they are supposed to, they don't bounce off yet I am not attached to the pedal.
Last summer I rode close to 500 miles clipped in, and while there are advantages to that, it isn't the only way to do it. I am currently back on my BMX pedals due to recovering from an injury.
Really all you need right now is a helmet and gloves. Bike shorts would certainly make your ride more comfortable - go with the most expensive that you can afford...it does matter where shorts are concerned. They should be the tightest that you can fit into - you don't want the padding to slide around when you are on the bike
Do you know how to change a tire? If not, see if one of your local bike stores might have a clinic where you can learn that. You will also need a small seat-bag in which to keep your tube and tire changing tools - there isn't much but it is important to have this on the bike at all times.