Invading Vermont would have to simply be a brief stepping stone to something more important. The only semi-secure area for the Canadians to use as a defensive measure against counter-attack from other Guard units (New York and New Hampshire) is Lake Champlain. The bad news is that you have the largest population center along that lake as well (in the state). The eastern side of the state has a very long stretch of reseviors, but there's so many access points across them that there would be little way to secure that border.
Another slight plus is that the Americans don't have an "easy" north-south access route from the lower half of the state to the upper half of the state. If Canada was able to control/secure I-89, they could essentially cut the state in half.
The big problem is you'd probably need a division or two of troops to take the state. If Canada is throwing that much at Vermont, then they've got a lot less to throw at the other "prongs" of your invasion.
Plusses are: Vermont is small. Travel is quick. They can hit things really quickly if they move with a purpose.
As Moehoender suggested, take out the airfield and known locations of guard facilities. The sheer quantity of people in Burlington will make it so that trying to "take" the town would turn into a long, drawn out battle.
Hit Burlington, make the airfield unusable. Blow 4 bridges along Lake Champlain and you've effectively cut that portion of the state off from New York. Blockade Burlington on I-89. Move southeast to Montpelier and take the governor. Get him to call off the National Guard. Make him appeal to the other states that Vermont is "fine" if no one comes in. As long as no other forces go into the state, the Canadians won't start killing Americans.
On the eastern side of the state, you've got White River Junction that needs to be secured, as well as St. Johnsbury. If Canada doesn't do that, you'll have New Hampshire National Guard coming over in the relatively near future.
On the southern end of the state, you'll have big problems. The best north-south route is I-91. You'll end up with Massachusetts and New York national guard units moving up, as well as any guard units in southern Vermont that might be in Brattleboro (I'm not familiar with where various guard units are located in the state). So in that regard, White River Junction again becomes a pivotal choke point. That's where I-89 and I-91 meet. If Canada gets and holds that area, they cut the fastest way north-south and east-west.
Then, depending on where the forces of Canada go after quickly trying to subdue Vermont, they can launch out of the state. If New Hampshire is next, they have two avenues of quick strikes. If they want to hit Massachusetts next to completely try to cut off the upper east portion of the U.S., they can head south down I-91. Doing that, though will be rather harsh, as they'll have to fight through the southern part of Vermont than has now probably been reinforced with NY and MA National Guard units.
Canada would also have to send a force to deal with Rutland, as it seems to be a fairly major stepping stone for NY into Vermont. So secure that area with a Brigade or something, either at the same time as Canada is going for White River Junction or a little before. Put good units there, as you'll likely be fighting against a couple of state's NG units.
As far as what Canada would be going for, I could only guess. If they wanted territory, they'd probably want to "cut off" a portion of the U.S. Vermont/Massachusetts would do it, as would just taking New York. New York is probably one of the hardest to take that way, but it certainly gives a lot more area to Canada. VT/MA is easier to take, but yields less land, less resources, and leaves a likely sizable NY NG sitting right next door.
So it all depends on what Canada is going for. They're not going to get a lot of food resouce out of this area, and land might be worthwhile, but you'll end up with a lot of people hating your guts. So unless you plan on wiping out a bunch of Americans, you're not going to be populating this area anytime soon. So you're just left with quick natural resources you can take out of country fairly quickly, and various materials that are already in-state that you can secure.
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