Modern Vespa

I recently bought a Et2 50 and trying to get it running. The bike was sitting for a while. At least a year. I have 3 known problems. Battery needs to be replaced. I was just going to buy one from local battery shop. Is there a preferred battery? Second I tried foot pedal start with start switch in off position just to see if it would turn over and immediately got a gas leak from air filter and tube that looks like an overflow. I checked form and found similar posts suggesting fuel tap. I unhooked gas line from carb and got a steady stream. Is this then a bad fuel tap? Where is a good place to pick up a replacement? Lastly I was thinking I should take carb apart and clean. Is this a good idea and is there a carb kit to do this? Any help is appreciated.

Welcome from the other side of the river!
I would check and replace all the fuel lines...do it one at a time, so you don't mess up......and use worm gear clamps, those ones that are OEM, are junk!
Drain all the old fuel out of the tank.....
Then, buy some carb cleaner in a can, and take apart the bottom of your carb, spray it, and the jets, make sure the float, needle valve, and float pivot pin is in the right place...DON'T lose any parts, and make sure the rubber seal gasket is on there right...along with everything else....
Remove the fuel tap, spray it with carb cleaner, then compress air...it probably just have junk in it, if not, new taps are not that expensive at the Detroit Vespa dealer, and they do wear out, spray the tank, and rinse with fresh gas...reinstall tap, hook up all parts, fill with fresh gas.... Fill oil reservoir, with good 2 cycle synthetic oil... I hope they didn't run it without oil!
Put in new spark plug....add a little 2 cycle oil in the hole to lube it up a little...and some fresh gas....
Buy a Yuasa brand battery...my last one lived 7 years in one scoot, and the other one is still alive in the 2009.....they are worth it...
Crank it...if it doesn't start check for spark....

Thanks. Sounds good. I will try this out. I have to head North to Detroit later this week so I will pick up fuel tap. What about a gasket/seals for carb when I take it apart. Do I need to replace these when I service carb?

Only float bowl gasket/o-ring on carb and it should be fine.

Thanks for the info. Hopefully I can get the parts in the next week and get her started.