Ah, I did just this a few years ago. One of the best things I ever did.
For a Lowland, drink Auchentoshan 10yr. The Three Wood is deceptive, as it is not made in the Lowland style, but heavily finished. Of course, it is the BEST of what comes out of the Auchentoshan distillery (in my humble opinion!) I gave away my bottle of (non-Three Wood) Auchentoshan it was so undrinkable.
There are a few Islands, but Orkney (Highland Park), Skye (Talisker) and Jura (Jura) are ones you could easily check out. As stated, HP 12 is good and within your budget, but Talisker 10 is hard to find for less than $65. Jura can be had reasonably cheap, but don't get the Jura 10. It is pretty one-dimensional. Just not a lot there (sea-spray with a bit of pepper, if memory serves me).
As for the Highlands/Speyside, these are a mixed crowd. There are so many variations on the theme. I think Balvenie 15yr Single Barrel (or 12yr Founder's Reserve) would represent the flavor profile well.
One GREAT Speysider is Glenrothes. Its Select Reserve really shows what a Speyside is. Light, crisp, floral hints and honey. Nothing overbearing.
Then you can taste a variation on that theme with some "wood-finished" offerings (Balvenie 12yr Doublewood, Aberlour 12yr Double-Cask Matured, Macallan 12yr Sherry, etc...
When you put on your big-boy pants, you can go down south to Islay, and drink Laphroaig 10yr/Ardbeg 10yr. Try the Bunnahabhain 12yr to get you started, but it is really just "Islay LIGHT." It's not the REAL DEAL.