Damp area around a plum tree

Tis very damp this far end of the garden. I don't know what to do with this plum tree "bed". It seems full of weeds/moss/forget-me-nots and looks awful. There seemed to be a lot of slugs around this part of the garden. Was thinking of putting a layer of weed supressant and stones on top? Would this be ok around a plum tree?

Had also thought of planting hostas around it through the stones as they like the damp-but so do slugs.

Anyone got any thoughts? TIA

 

For preference, weed suppressant or perhaps hardy annuals that won't require a lot of soil disturbance. If you start digging round plum tree roots, they sucker like mad.

 

Thanks @noisette47 I'll clear it of weeds and put supressant down. There's a load of suckers already!

 

Eeeek! Try pulling them out....if you pull at an angle, you might be able to detach them complete with the buds that would otherwise produce the next lot of suckers! Failing that, cut them off as close to the root as possible. Hope it works out

 

Id not realised what a problem they could be. Just read up on them and they sound a nightmare