New bike problems

[Jhncf]

Hi guys, was looking for some help with my new bike and thought this forum would be the best place to ask. I bought a 97 XJ600 Diversion yesterday, test drove it and all was fine, parked it up last night and when I checked it this morning there was some oil on the road under the bike. I checked where it was dripping from and its been coming from a black hose under the bike. The bike was difficult to get started, got it started and it died when I was revving it a bit (think it was still cold) then wouldn't start again, sounded like the battery was dead. Bump started it rolling down a hill and it ran fine, turned it off and it started again no problem, done this a few times and all was fine. The bike also jumps when I click it into 1st from neutral. Sorry about the long post but I know very little about the mechanical side of bikes and would like to have a go at repairing I myself, thanks in advance!