After about a year of reading and reading about welding, and which kind of welder i'd want, I got cold feet and let it idle for about 6 months. Then, just a couple weeks ago, a welder came up on Craigslist that was priced so well I couldn't ignore it.
I picked up a Lincoln Weld-Pak 100hd. It can do up to 1/4" thick steel and can be converted to MIG as well. The flux-cored wirefeed is serving me just fine so far. I made up a welding table and some mobile bases for my woodworking tools.
It was stupid easy to learn to use. Patience and a good view are really only things I've had to worry about. The voltage and feed speeds take a wee bit of time to get used to, but not too bad. My first ever weld was pretty decent. I've had worse welds since, lol. There are a couple of great YouTube videos instructing the basics of welding.
Part 1:
http://www.youtube.com/watch?v=lzBGZaS1apw
Part 2:
http://www.youtube.com/watch?v=sMdQT-eswYY
These two got me a feel for what to expect and listen for. Then just actually gluing steel together helped to fill in the blanks. Playing with scrap is a great way to learn stuff
As for the other equipment you'll need...
Leathers - gloves and apron. I've heard some pros do without the gloves but as a newb, I'm happy to keep my fleshy bits away from scalding stuff.
Clothing - wear natural fibers, NOT synthetic plastic stuff like nylon or polyester. All-cotton long-sleeve shirt and blue jeans.
Shoes/Boots - leather - not plastic. Again, if a glob of slag lands on yer foot, you would prefer to have natural fibers rather than napalm
An auto-darkening helmet is NICE but not absolutely needed. You can get away with the little puppet mask that comes with the cheaper ones, but I sure like having both hands free. The regular flip-top masks that are always darkened work fine, if a bit cumbersome. If you don't mind harbor freight, I think they still have an auto-darkening one for $49 - with a 20% coupon, that brings you down to just over $40 with tax - nice deal and it works quite well.
Other equipment kinda depends on what you're gonna be doing. An angle grinder is very helpful in most applications. I may pick up a 2nd, because I really like having a wire brush on mine, but also need the grinding wheel quite a bit. Not having to change over is convenient
A set of MIG pliers is handy to have for removing the tips and clipping extra wire. If you ever go full MIG, these pliers also come in handy for keeping the tip clean, too.
Clamps and workholding as needed. THose magnetic triangles are hamn dandy to keep around, though sometimes you can just hold the items by hand. Special vise grips for getting up and around obstructions is also handy. Some guys use C-clamps with special copper threads because the spatter doesn't stick to copper too well. So far, I've gotten by with just vise grips and magnets.
A welding table is nice to have if you're building stuff that's not attached to something big and bulky. It's also a great first project. I built mine out of some 1 1/2" angle iron and a 3/8" thick plate for the top. It's also helpful for keeping all my welding stuff organized and portable.
I dunno what gauge the Vespa frames run, but even a small 100a welder like mine (which runs of 120v) shouldn't have much problem with that. Real thin stuff (like below 18ga) may need MIG, though.
HTH