I would sooner do retirement planning by way of lottery ticket, and not even the fun kind where you buy up enough during a rollover or something to make it worth your while.
As far as legality goes then private land, public land, permissions, disturbing plants/wildlife make things tricky but not impossible. Many places will have a compulsory first purchase* by the government to stop things from vanishing into private collections if it is interesting enough (though rates are usually nominally what the auction of things would get). 99% of things you hear about are complete random chance by a farmer (usually someone buried their money/valuables because banks back then were not so reliable, went off to a war, never came back and failed to tell anybody), a more scientific approach (usually a hot summer sees the foundations for some Roman villa turn the crops browner around that area more as you lack water because it is stone), or a road is being dug up and some village it once ran through that vanished during urbanisation is found). You might find things in marshes but most sites of notable battles on them have already been dug up, and most marshes got drained in the 1970s or so when such feats became possible (not to mention nobody buries things they expect to get back in a marsh, and most marshlands were the poorer parts of a country anyway). You could up the odds a bit by looking at ancient maps and going around various castles that no longer exist (stone is valuable building material, as are large seasoned timbers, so locals tended to use whatever was available).
*inside houses also gets fun. Story around here is someone was doing some rennovations, chipped a wall off and found a very old (12th century I believe, which is old -- houses back to the 1600s is nothing strange at all but few are that old) wall painting. As listed buildings would make life a nightmare then oh dear it was just rubble.
Now if you did want to do something like this and were willing to bend laws I would go a bit further south. There are places in Egypt that are built on top of ancient Egyptian stuff and plenty of locals make some extra cash illegally digging things up there. Chances of some little statue being found as opposed to pottery fragments... hard to say.
If you wanted to stick to more legal things then you would probably make more looking for modern stuff on beaches (people lose rings and necklaces all the time) or going round after festivals.