Looking to buy as well and think that putting down 20% is the way to go. Any chance you can get a loan from parents? I think they can gift you $13k each tax free.
As for rates increasing, I would guess the earliest it would happen is Q4. I also feel that home supply will increase pushing prices down this year. I believe the last Case-Schiller index was down and that was for January. I’ve been watching homes in the lower end ($400s) a lot these past two months do notice that prices are coming down. Once all the sideline buyers are done buying prices should fall further.