I won't claim to be any sort of connoisseur, but I do enjoy a nice scotch. I'd say you've got a good starting point; I've always found Glenlivet to be a good "safe bet" - pleasant flavors, smooth finish... mind you, if you like Glenlivet 12, you should really try the 18 year old... I've had Glenlivet 12, 15 and 18, and those extra years definitely add something!
Other rather nice single malts I would suggest...
- Oban 14 is nice - I find it has an interesting chocolatey note, almost like a "dessert whisky".
- Scapa 16 is also rather interesting; light, with heather honey characteristics (and I swear I caught a whiff of coconut from this!)
- The Macallan, in various incarnations, has always been good to me.
- If (perhaps after a few "safe" malts) you're feeling adventurous and want to venture cautiously into Islay territory (think lots of smoke and peat), you could start with Bowmore for a comparatively gentle whiff of peat; Islay whiskies are not for the faint of heart, but once you get into it, you'll be delighted to find what Lagavulin, Laphroaig and others have to offer!
Admittedly, these are only my personal preferences, and I honestly don't know if they fit your price point; I live in Norway, and the price of a decent bottle over here is around $90 at the current exchange rate - I suspect these are noticeably cheaper where you live.
Also, I'd like to wish you welcome and congratulate you on discovering a love of whisky that's sure to grow into an obsession; there's some amazing stuff out there!