I've considered this myself, but at this time I just don't have the resources (especially the time) to go down this path right now. That said, I have looked into it a bit, especially the costs involved, and realistically the firearm isn't really the biggest cost; I figure a non-restricted course alone costs more than a basic .22. Range costs are also a big factor unless you have easy access (or the time) to use crown land.

That said, looking around at a couple Canadian online retailers, the .22 / .410 combination that I could find (Savage Model 42) runs around $470. I've been watching "Out of the Wild: Alaska" recently so I think its kinda cool & see the appeal.

To follow the advice of others here, which seem to make a lot of sense, you could get a single-shot shot gun & a semi-automatic .22 for around $350 (H&R Pardner in 12 ga., 20 ga. or .410 & a Marlin 795), for example. For more fun, you could go the 10/22 route, but they are more expensive (starting around the $250 mark), but you can get high-capacity magazines for them (there are no restrictions on rimfire magazines in Canada). Take down models also seem cool, so that might be another consideration.

To get into deer, I'd personally think hard about adding a centrefire rifle and would want to budget at least $400 - $600 for a decent entry level model.

I have no clue what the used market is like, I haven't looked into that. But I kinda assume that the lower the cost new, the lower the cost used, but I know that doesn't always hold true for all things.

All that said, keep in mind this is coming from someone who has only read the advice of others around the internet and isn't yet moving beyond the curiosity stage of research.
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Victory awaits him who has everything in order — luck, people call it. Defeat is certain for him who has neglected to take the necessary precautions in time; this is called bad luck. Roald Amundsen