Hello from me, fellow pig keeper, up in Scotland
They'll ALL dig, so if your trees are less than 10 years since planting, keep the pigs away from them
Even my short nosed Kunekunes managed to uproot a not too small willow
I'm a big believer that there's a breed for each person/set up, you just have to figure out which one it is both in theory and practice.
We've had Large Blacks, Berkshires, Tamworths, OSB's, Kunekune and Saddleback/GOS crosses - all lovely pigs and great pork, but you'll find that there's one that just 'fits' you best
Get a few different breeds in the spring and raise them to slaughter, see which ones you like best and take it from there (or do exactly the same thing the following year with another range of breeds
)
Berkshires and Large Blacks are in need of more help in terms of numbers being kept and bred, so that's a plus for them
If you're new to pigs the general advice is to start with a lop eared breed, so not Berkshires (but it has to be said my two Berkshires didn't give me any trouble) GOS pigs and pork have the TSG status, so it's a plus point when the time comes to sell..... See what I mean, the arguements for and against each breed could go on for pages and pages but until you've kept them and managed them you'll not know what's best for you and your set up - so go on, get a few different breeds and see which ones you like best.
They should all be okay with the ground ivy I think, pigs are normally quite good at avoiding things which make them ill but I've no ground ivy here so can't tell you for sure
HTH
Karen