Believe it or not, the online photopea editor seems to have full PSD support: https://www.photopea.com
A number of other Photoshop alternatives exist. I personally prefer Affinity Photo, and it imports PSD.
As to what filetypes, you really can't go wrong with PNG, which has transparency support, which is needed for lots of effects. I'm sure others will respond with their favorites and add more to this. Best of luck.