Ive bought many basses online before playing them and some are my favourites. I would always be sure to know what the radius and neck profile is, pickups etc, before buying, but having a knowledgable seller that understands your needs and expectations really helps in making sound choices that you don't regret.
Jazz basses, like any other bass, can really vary from each other, but if you get the right one in your hand, they are amazing. Same goes for a nice P bass. Personally, I like a early 60's skinny nut neck profile, with true single coils. I like the aggressive tone and responsiveness they have versus hum cancelling J pickups. Pair one of these up with a high quality tube amp and bingo.