Hey Carson.
Group rights can be totally confusing, right? I think there are really two issues here:
1. Your land and what group it's under. You shouldn't need to add your landlord to your group in order to set your rented land to your personal/business group. (And as others said, he definitely never needs to be owner, and shouldn't be unless you are business partners, too!)
2. Your object permissions.
If you just rez your vendors and stuff out of your inventory as normal, nobody should be able to move them or take them. The obvious exception to this is for people that you've specifically granted edit rights to, and you will know if you've done this because SL will shout at you that it's a really big deal to give someone rights before it lets you ok it.
If you set your objects to group, they should still be safe and sound. Setting stuff to group is usually the most useful in terms of which objects are allowed on a parcel. So like... you might set your land so that only the group can rez on it, and what happens then is that stuff that isn't set to group gets auto-returned. Again, if it's just set to group, I'm pretty sure nobody can screw your stuff up.
If you DEED your objects to the group, then other group members can potentially take and move the objects. For them to do this, they would also have to have this ability enabled in the group settings, under Roles. In general, unless you really mean to share an object with someone like this, you should never have to deed anything. (I've been in SL like six years and I've never deeded anything except out of curiousity.)
Hope that helps. If you have any other questions or you need an oldbie to come help you play with permissions for a day, just give me a shout. And good luck with your store!