To build on what Chris said: the Amiga is literally a huge cosmos of awesomeness, but, as you already know, it will take time to explore all the main areas, let alone all the nooks and crannies.
The obvious answer is to follow the "best of" and "most underappreciated" and "most forgotten" lists that you'll find littered about the net-inter-netz-webz. Some of these lists are lame, but, HEY!, they are really for folks who are just beginning to learn about a new platform.
The Amiga may not have been huge here in the States, but it's hard to ignore the passionate, awesome developer/indie support the platform had (has). The great thing about the Amiga is that you do not feel like it is a dead, sterile topic for archeologists/historians only...tons of people are actively playing and enjoying the software (yes, 99% is via emulation, but that's true for all the older platforms, I reckon).
Personally, I am more invested in Commodore 64 (because I grew up with it), but I intend to spend more time with Amiga in the future.
The great thing is that even if a game for Amiga doesn't hold a lot of replay value (AKA it sucks), it still has a lot of interesting stuff to appreciate (art, music, history, etc.). This cannot be said of sucky games in general (for most platforms). In general, developers *seemed* to put lots of love and care into their Amiga offerings. This may or may not be quantitatively and/or qualitatively true, but it certainly *seems* that way. Net result? Even mediocre games *seem* like they were half-loved (again, art/music). This has led some silly observers to declare that Amiga library was "style over substance" but this is total garbage. If this claim is true for Amiga, it can be leveled at many platforms with much, much worse crap:quality ratios.
At times, I have seen an anti-Amiga sentiment amongst some folks, but haters are gonna hate. Let them.
BOTTOM LINE: Hell yes, the Amiga is worth it. BUT I AM A C64 LOVER, so...