Decent 4 jaw chuck/jaws: $130-200
Collet chuck: $90
Mandrels: budget $35 per diameter
Turning tools: Budget $150 for a basic selection at PSI's prices
I imagine if you add up the cost of the tools on most of our turning benches you're going to approach a couple thousand bucks. The lathe is a small investment compared to all the other stuff you'll find a need for.
The bed extension is nice but is by no means necessary. I've never had one and do not have the need for one. They are available for Jet as well as Delta. I agree that between Jet and Delta lathes, it is a Ford/Chevy debate. Either will do the job and do it well.
KC speaks he truth... all of those accessories, sandpaper, finishes, and LOTS OF OTHER GOODIES are going to blow the first couple dozen drafts of your "start-up" budget straight to Haties. You don't buy all those things you want all at once though. Think of it as a collection of stuff that you'll build up over time. It took me 6 years to get all of the things I ever wanted, yet I have another bucket list of things I want to get eventually... and I'm a minimalist by nature. Woodturning is a bottomless pit, so for now just figure out what you want to turn and the tools that will
require, and start there. On the upside, with the tools and accessories you need to make friction calls (plus a bowl gouge), you can also turn bowls, boxes, and a lot of other cool things.
just for giggles, my start-up list would go something like this:
12" swing lathe (Rikon, Delta, or jet)
4 Jaw chuck (Barracuda 2 or Nova G3) tip - the Barracuda 2 comes with several jaw sets, the G3 comes with just 1 set
1 each of the following chisels-
1/8" or 3/16" parting tool
3/4" roughing gouge
1/2" spindle gouge
1/2" or 3/4" skew
3/4" square end scraper
3/4" round nose scraper
3/8" bowl gouge
8" slow speed grinder
Wolverine style sharpening system