Depends on the tree (You may have said ^ but I’ve scanned through) but if you leave the stump you could be dealing with suckers forever more.
Having removed many (and have many more to do, including one on a sandstone rock face that the roots have caused big fracture lines in) then definitely go for the easiest option – Digger! (I’ve not used one but always wish for one) otherwise prepare yourself for some graft with a spade, pry bar (couple of handy bricks too for a fulcrum), loppers and a mattock.
Listen to Timber and Glasgow, it’s their job, I just do it for free