Santorini Assyrtiko is a great wine, but production is limited by the size of the island, and the market is now recognising the high quality of the wine, so it is not cheap.
Personally, to understand what Assyrtiko is about, I would start with good quality wines that are not designed to be too fancy. Gaia Thalassitis is such a wine, it’s made in stainless steel, widely available, and relatively cheap, from around £22. It’s sharp as a razor, pure and precise. That’s Assyrtiko - without oak, wild yeasts, lees aging and all the other things that might be used to make more upmarket wine. As you might know, Gaia, is now a pretty well established winery, with a number of locations (two I think) in Greece.
The Santo Wines basic Santorini also shows the grape well at a lower price (about the cheapest Santorini you will find). Santo is a coop, but not to be sniffed at - it really kick-started modern wine production on the island, so was very influential. However I think most people would notice the drop in quality from Thalassatis.
Another favourite of mine that is not too showy, but IMO damned good, is Vassaltis Santorini Assyrtiko. I think it is their “basic” wine, from around £32 in the UK. This too is clean as a whistle, but shows more complexity than the Thalassitis. Vassaltis is a relatively new producer on the island and considerably smaller, but doing great stuff.
At the very least I think those wines are a good place to start. Personally I find myself returning to them too. But there are plenty of other styles to explore, not least the sweet Vinsanto.
Agyros and Hatzidakis (mentioned above) are both older family businesses on the island, and well-respected. Sigalas is another good traditional name on the island that springs to mind. I tend to find them interesting rather than necesssarily the best, but that’s just my personal taste - they are certainly worth trying.
I would say Albariño is a pretty good point of comparison for Assytiko. Another one is Alsace Riesling (German wines are too light). There are of course differences, but I think they both indicate the ball-park feel of Assryrtiko.
Finally, do visit if you get a chance. As with the wines, it is now very popular and not cheap. I would suggest going early or late in the tourist season to avoid the tourist hordes (especially cruise ships). But it is stunningly beautiful, and with great archeological sites too.