I have and old avid 185mm rotor want to chance to shimano 180mm need advice

So I have an old bike and I’m saving for a few one but the brakes on this one have give in there’s many things wrong with them as they are old as hell I have a 2009 rockshox reba SL with a 185mm adapter, avid Elixir R brakes wi th avid 185mm rotor front and avid 160mm rotor back.

So I am changing brakes and rotors, I am new to this so im unsure of the adapter I will need as I was going to change to 180mm rotor on the front.