I have 2 views on this:
1st view is, as of right now, no training should be mandatory. Defiantly should be encouraged though as we will be on earth for a long time. Most of us here, won't get to go into space...but our kids or grandkids just might. So if anything, it would be to set a good example to them (and the rest of the world if a optional program was up and running by the administration).
To teach them about Asgardia as a protective nation to all humans not a nation that will strive to militarization and mistrust.
2nd view is, in the future, if we end up being on a space station or ship, it would be unpractical to send humans back down. rehabilitation to get used to the gravity would take some time or even kill. One option would be to leave some folks on earth in their own city, have them well trained as potential peace keepers or something along them lines.
However with that being said up in space, everyone should be trained in first aid , basic hand to hand and engineering/IT skills. Police force should always be a must, people are unpredictable at the best of times.But i do not think they should be armed. Maybe a highly trained and equipped anti-terrorist unit should be the only ones that have access to firearms.
In regards to fighting aliens i don't think hand to hand would be an issue, they would just need to put a hole in whatever we would be living in to kill us off. Instead of combat ships like you see in films, perhaps some type of drone to protect us from them nasty green men?
Although a defense (inc anti-missile) system on anything that we are living in would be a plus if that kind of scenario ever happened.