The Tartan 34 is a pretty nice boat. They sail well for their era if not too heavily loaded. They were reasonably well built for their day. They had a number of layouts and the traditional aft galley layout could make a reasonable offshore layout. While not that good in light air or a chop, they are otherwise pretty well rounded designs.
The bad news is that they are quite cramped for a 34 footer and do not have great gobs of storage space. They were not set up to handle the kind of large and redundant ground tackle that distance cruising requires and most still have Atomic 4''s. The other issue is that these are roughly 30 year old boats and they are getting quite long in the tooth. Unless the prior owner has been diligent in doing long term maintenance, to put one into shape to be a decent offshore cruiser could easily run $30-40K over the purchase price of the boat.