So, I might be moving to a new garden to start fresh (not too soon though). Now, ideally I'd like to move some of beloved plants from my old garden to the new one. But since I've had so much trouble with diseases over the last two years (especially fungal), I'm doubting whether I should. I don't want to infest my new garden with possibly the same ones.

What I'd like to take with me are some ferns, grasses and ofcourse my Siberian/Japanese irises. All of those are not prone to the diseases themselves, but nevertheless the plants that are I still would like to grow again. Should I take the risk?

I would take anything that you love and want to keep. Remove them before you list the place for sale. I've done that many times, and if we ever leave our present place, many of my cacti will go go with me. Some are very old now.

I second potting and taking what you want. It could be your soil was the problem or maybe the weather, but if you don't take the ones that are special to you then you will probably regret it.

Quarantine. If fungal, treat before moving, your new garden could have issues exactly opposite of what you have now, or the same. Pots will work until you know