My first rifle stock is AA myrtle. It is easy to carve and inlet, sands easily, and has been relatively stable over time. It does check faily easily, but it looks beautiful when the light hits it right. Use a light-colored stain to bring out any figure or grain. Black myrtle has dark steaks through it but otherwise is the same blond wood.
Walnut is commercially grown, so it is one of the few sustainable harvest woods, the main reason it was used for so many things. It also has cross-linked grain, which makes it a bit stronger and harder to split. There are numerous varieties of walnut, each with their own properties. Here in the States we use a lot of Black walnut for gunstocks, but European walnut gives us several varieties as well (Bastogne, English, French, Circassian, Turkish), and there are Asian, African and South American walnut woods (not sure if they are all true walnuts, though). Claro walnut (California black walnut) is not very dense, but it is pretty when you get a nice piece.
Most commercially available maple is commercially grown (sugar maple), but there is enough wild maple on the market to make it hard to say one way or the other. Maple is pretty, easy to work and sand, and about the same density as walnut, but is not cross-linked. Most maple blanks I see are sugar maple (eastern maple, hard rock maple, fiddleback maple, etc), but you will find Western maple as well (big-leaf maple, silver maple).
Various fruit woods and nut woods are suitable for gunstocks, thy're just hard to find in a big enough piece to use for a gunstock due to horticultural practices (nobody wants to pick fruit 30 feet off the ground). Apple wood is beautiful, but most commercial orchards do not let their trees get past 20 years old, not big enough to yield a slab large enough to carve a gunstock out of. Mulberry wood is pretty, but there is not a lot of it grown any more. Pear wood is nice but rather bland. Hazel wood is very nice and beautifully grained, but you will have trouble finding a piece big enough to make a rifle stock. Cherry wood is beautiful, plum wood is pretty, olive wood is kinda bland. There are a lot of woods you can use.
Tropical woods are interesting but expensive. Years ago I had a customer ask if I could make him a stock out of purple heart. When I checked the price for a slab that thick, it was pricey. But it would have been beautiful.
Legume woods can be really pretty, but a re generally hard to work. Koa is a type of locust tree from Hawaii, it can be bland or beautiful. Mesquite and desert ironwood are pretty, but finding a piece big enough for a stock can be like finding a four-leaf clover. Paulonia has purple-ish grain if you're into that type of stuff. Madrona fiddleback is pretty but brittle. Manzanita is pretty. There are so many, but walnut is cheapest.