If you can find a Remington 788 in 30-30 at a decent price, then you will truly have a very good repeater. A 30-30 in a Handi is a very good shooter too, I have one and like it very well. Never owned a Savage 340, but have had a 788 in 222 and wish I never let it go. Had one come up for sale locally, they wanted $475 for it. I can build a new Savage for not much more than that so I did not get it.
Good Luck and Good Shooting