CMR - First, welcome to the forum. Second, what type of wood influence are you looking for?
I will assume, if you're new into Scotch, that you're coming from Bourbon and/or wine. If so, the wood characters dominant in Bourbon is vanilla and caramel. Vanilla is also prevalent in many new world red wines, especially California cabs and Aussie shiraz, as well as cedar notes.
Where the major flavor profiles in spirits aged in barrel are derived from the spirits' interaction with the barrel during maturation, 99.9% of Scotches are aged in used barrels - with American Bourbon barrels being used about 80% of the time.
Back to my assumption of where you may be coming to Scotch from, I would suggest trying a few whiskies with maturation in different barrels to get a different perspective different barrel influence. Though don't expect the over-the-top wood notes you get from Bourbon, as Bourbon must be aged in new barrels. Those new barrels have more of an influence than used barrels because the new wood has more to offer. That said, I'm going to recommend a couple whiskies which are easily found.
Try Macallan 10 Fine Oak. The Fine Oak line was first released in 2004, and is a line of Macallan aged in ex-Bourbon casks.
It is/was somewhat controversial due to Macallan's insistence from the beginning of time that their spirit was best aged in sherry cask and sherry cask only. What annoyed people in the industry was, as global sherry drinking declined (and continues to), it was long recognized in Scotland that the supply of Sherry casks at some point wouldn't match Scotland's demand. Especially since the Scotch industry was expanding in the face of sherry's decline. So when Macallan released their Fine Oak line, it confirmed what many in the industry knew, and it annoyed many because Macallan came out with an entire line from 10 Yr to 30 Yr. Indeed Macallan had been aging in Bourbon barrels at least 30 years longer from what their mouths were saying; and it is suspected they had likely been using some Bourbon casks when bottling their traditional line for some time, as many experts recognized a change in the traditional Macallan bottlings in the early to mid 1990s from what the line was prior to their now publicly-embraced use of Bourbon barrels.
Also try Macallan 12. This is Macallan dominated by sherry cask.
From these you'll get a sense of what ex-Bourbon casks lend in terms of oak influence and what sherry butts lend. And you'll see it against the same spirit. The 12 will drink sweeter like a lot of Bourbon, though with very different flavors.
Aberlour 12 Yr. is another sherry cask aged whisky to try. If you find it, Edradour 10 Yr. is pretty beefy with good wood heavy characters. Isle of Arran 14 Yr for a lighter very balanced whisky. Glenfarclas 10, 12 or 15 Yr. Glenrothes Select Reserve. These are a handful with good wood character which should also be fairly easily found.