It would be easy to suggest an impressive cellar of classic wines - that you might not like at all!
There is sense in sampling some wines to get a feel for style, and for this I would say lean towards the value but typical end of the market. No sense in buying the grandest names. Treat these as wines you probably won’t age very long, but will be the forerunners of wines that you will age.
Where to start:
France
Definitely get a feel of Bordeaux ‘right bank’ vs. ‘left bank’. For the former, try one of the richer St Emilions against the generally more classical (but user-friendly) Pomerols. This will be a useful pointer to future purchases. For the latter, much more choice, but avoid shooting for the grandest, as some more modest wines will give you a good feel based on a relatively young wine. Maybe a wine from Margaux the region (not the Chateau) - personally I’ve had decent success for modest money e.g. Château Deyrem Valentin.
Chateauneuf du Pape is an interesting place to start for the Rhone, not least through the heated recent discussion here (I think the thread started by A. So would be interesting to read). Fundamentally this area could give you a really good stylistic checkpoint. If you like the richer end of Cha… (I’m too lazy : C9dP) then not much point in exploring Cornas, St Joseph or Cote Rotie yet, but they may come later, or earlier if you prefer one of the more traditional C9dPs. Don’t ignore Gigondas for a taster bottle either, and these are rarely at the lush end of the scale, but often combine good vibrant fruit and good grip. Get some ideas of producers/wines from that thread.
Burgundy. I’ll defer to others here. It’s an expensive region, so easy to blow a lot of money very unwisely. Personally I’d defer this one until you’ve explored other regions.
Beaujolais might be a shock to the system and well worth trying before buying anything. Prices are still very fair, but it might not be love at first sip. Indeed I think your head has to be in the right place to start to enjoy Beaujolais, as it may be very different to wines you know & love, hence going in with a very open mind will help.
Don’t ignore Southern France: Provence, Languedoc etc. and many would make more natural entry points for a palate more attuned to new world winemaking. Plenty of these perform rather well in the cellar.
Italy
Barolo (and Barbaresco) can again be a style you might not ‘get’ immediately (or ever). Try a few before buying any volume, and be aware that on release there is often good fruit partially obscuring firm tannins, but that they can shut down as the vibrancy of the fruit drops away. Assuming you can find a bottle of Produttori del Barbaresco (standard Barbaresco bottling with the emblem of the tower) open it with roast beef or lamb (or a steak) so you have something to fight the tannins. It’s a good benchmark wine, true to the region and should be easy enough to get hold of.
Brunello: I reckon a more promising entry point for a new world palate, FWIW I find this denomination typically less enjoyable than Vino Nobile di Montepulciano & Chianti, but then I prefer the grip in those wines. Different strokes for different folks, with more people preferring Brunello & so it costs more.
Other wines:
Super-Tuscans might be derided here, but they are a great entry point for someone used to Cali Cabs etc. They will taste different to what you’ve experienced and (IMO) the good ones do have a sense of being ‘Italian’ though I really can’t put that into words.
Valpolicella / Amarone. Essentially the same grapes, but the latter has significantly more grape drying, which really turns the dial up to 11. For many people Amarone is one of the first wines to make them go ‘wow!’ because the intensity can be seriously impressive. Valpolicella still has stronger (slightly fresher) fruit and a good degree of richness, but you’ll get a touch of bitterness with (usually) good acidity. The comparison of both from the same producer can be interesting. If you see a Valpolicella ripasso, this is likely to be aiming for the middle ground between the two, but styles do vary. For a cheap widely available wine, consider Allegrini Palazzo della Torre or Masi Campofiorin. IMO neither is a great wine, but both give a sense of what the wine style is about and should be easy to find & taste without meaningful cellar time.
There are a huge amount of wine styles in the two countries, enough to satisfy a lifetime, and we’ve not even mentioned Portugal or Spain.
I will re-iterate the earlier advice though - don’t fill up the cellar until you’ve sampled ~ 2-3 bottles from that region and are excited by them. Any fool can ‘curate’ a cellar of renowned classics (just pay a visit to the Peck wine shop in the basement of the famed food store in Milano to see this achieved), but the intelligent person collects a cellar with wines that personally interest them.
regards
Ian