Short version: Great lathe, everybody who has one seems to loves them, you'll be very happy with it and likely never need another lathe.
Long version:
If you've never been "a turner" before, that seems like a lot of lathe to try it out. The 3520 specifically, IMO, is quite expensive for what it is.
When I started turning I got a cheap, used lathe. After using that for a couple years, I got another, slightly less cheap (but still cheap) used lathe (which is what I'm still using today). Only now (some 10 years later) am I looking for an upgrade. Jet's 16-42 is at the top of my list at the moment. I considered the PM3520 quite a bit as well, but at the end couldn't justify the massive price increase for what amounted to a little extra throat capacity and some beefier castings. (Que the rage from 3520 owners
)
From NCWW archives I've read that any machine is only part of the issue. Everything else you need to be successful can be equally expensive.
You are right on here. Over the years I've spent many times the money on tools and 'turning stuff' that I did on my lathe. Good quality tools, chucks, jaws, bits, grinders, wheels, jigs, thingers and whatsits all are expensive.
Again, this is all my opinion but I'd say that the lathe your using will account for something like 20% of the final product. The tools, the technique and the turner all make up the lion's share of what makes good turnings.
If you're looking for a top list of accessories...
Chuck and jaws: Get a good one. I favor Oneway's Talon and Stronghold. They are built great, have a number of jaw options and will last a lifetime. I know others have great things to say about Vicmarc's chucks, as well as the Nova series. All should serve you well. If you want to do bowls, get the 'cole' or 'jumbo' jaw sets for the chuck you get. These let you easily reverse mount and foot bowls without a lot of hassle.
Grinder/Jig: If you don't already have one, get an 8" bench grinder and a 120grit wheel. Then get the Wolvarine system and Varigrind sharpening jigs. I can't emphasize enough how much of a difference these jigs make in getting a good edge on your tools. I toiled away far too long manually sharpening my bowl gouges before getting one of these jigs. In my turning progression, getting my tools sharpened correctly (using these jigs) made the single biggest difference in my results of ANYTHING.
Tools: There a zillion schools of thought here on what/who make the best tools. You'll see a lot about carbide-cutterhead scrapers (easywood tools, etc). These are not bad, strictly speaking. They'll get you up and turning quickly. However I think they tend to stunt skill development in new turners. With those tools you can sort of just shove them into the wood and get reasonable results. The cost is that people tend to never learn good tool technique or control. They have their place, don't get me wrong, but there are a ton of traditional hss tools that will serve you just as well, if not better, over the long haul (and cost quite a bit less).
On HSS tools: I love the Thompson lathe tools. They're phenomenal steel and priced very, very reasonably. Doug Thompson makes every tool you could need.
Too much info? Sorry... long winded....