You can't 'be recovered'. You could say be cured/healed because someone/thing is doing it to you. I hope I (will) recover soon (hope suggests the future so you don't necessarily need 'will') I hope I (will) get/feel better soon.

“I hope I will recover soon” is the most common phrasing.

Hi, Both of these are correct, however it depends if the recovery is a definite or not. If it is, then the second one is correct and if it is a wish to be recovered soon, but not definite, then the first would be correct. The surrounding context is what would make either one of these correct. Hope that helps.