I'd recommend a 12 gauge as well. Quality target loads in 7.5 shot use hardened shot and quality components that pattern well and cost less than the cheapest .410 ga loads out there. If you're shooting them on the fly, the 12 gauge will still challenge your skill while lessening the chances of a crippling shot.
With the exception of more secluded areas where grouse are very tame and easily shot with a .22 or .410, they tend to be fast flushing birds that are challenging enough with a fullbore shotgun. If you come across a reasonably priced 20 gauge, they're another good gun, and sometimes you'll be able to find the target loads at a cost similar to 12 gauge. A good 20 would be lighter to carry and fast handling as well, though it would be less versatile if you decide to want to hunt waterfowl or other game in the future.
A good compromise if you can find one are the Savage 24 rifle/shotgun combos. The older models came in .410 and 20 gauge with .22LR, .22Mag, .222 or 30.30 barrels. The more recent models (with synthetic stocks) come in 12 or 20 gauge with .22LR, .22hornet, .223 or 30.30, plus come with a choke tube in the 12 gauge model. I have a 12ga/22Hornet model that sometimes makes it out to the woods.
Whatever shotgun you buy, I'd recommend looking either for an open choked gun (i.e. improved cylinder, perhaps modified on the second barrel of a double) or one with choke tubes or choke device. Though some areas afford shots at longer range (perhaps some mountainous areas of B.C.?) usually the more open choke is better. If you're stuck with a full choked gun, as many older shotguns tend to be, you could buy spreader loads (about $10 a box here) or eventually get the choke opened up by a gunsmith.
If money is an issue, sometimes you'll find an old pump gun in the EE with an adjustable choke device for about $150 shipped (I know, I just got one myself, and saw two others for a similar price when looking). Some cheap bolt action shotguns have adjustable choke devices, and decent used side by sides (usually just in full & modified choke though) can be had for about $250-$300 shipped from places like Tradeex. For new guns, there's several 12 and 20 gauge pump gun options from Mossberg that will probably ship to your door for under $300, a bit more for a two barrel combo for shot and slugs. The Remington 870 Express pump action will cost a bit more than the Mossberg.
The shorter barrelled Grizzly pump actions from Canada Ammo or Norinco HP9s are popular with many people on this site ($250-$350), especially as a hiking or all purpose shotgun, but the 12.5 and 14" barrels would not be as effective for hitting birds at longer ranges (not because of lack of power, but because a longer barrel makes it easier to follow through and hit a target at longer ranges). Not a problem if the birds are flushing at your feet, but less effective if you're shooting at 25-35 yards.
For .22s there's all sorts of options, but at the very least there's lots of old single shot and repeaters (i.e. Cooey) that can be had from anywhere from $60-100. It's not a bad idea even if you get a shotgun for grouse, since even if you don't hunt with it the markmanship skills gained by practicing with a .22 will be helpful should you decide to hunt big game with slugs or centrefire rifles in the future.
The locals where you live will give you a better idea of the typical conditions in which you'll be shooting grouse and the best shotgun for the job. Hopefully, this will give you an idea of all of the options and things to consider.
With Regards,
Frank