The single player missions and the online missions never cross over. Obviously though they are set in the same city and at the same time (I think from memory online is set at, or just before, the start of the offline story) so that is why you get missions from Lester, Trevor, Lamar etc.
As for partying up - if you either drive/walk in to a mission on the map it will load the lobby. Alternatively, if you press option - online - jobs you can load any job up from there. Once in the lobby, you sometimes will get put in to an existing one or be host and you can pick the options. If you're host, you have options to invite players to the mission. Some of these are handy options like party members or friends playing GTA. If you are playing solo though you can auto invite or invite skill matched players which sends the invites to loads of random players. As Diddums said though, be prepared to get very frustrated with randoms.
One thing on the property / garage front - It is worthwhile getting one as it opens up options such as the heists and ability to keep cars but you can own multiple properties (I assume you can also sell an old one if you want also) so it isn't necessary to instantly buy the most expensive/largest one.
Something to note too, you can sell 1 car per day at the custom shops. Like owning cars, you can't just steal a high end car and sell it but any 'normal' car you can. It doesn't net much, only a few k, but it is easy and quick money.