If you are wanting to deploy just one or two ships with logistics you should use an actual logistics ship (Guardian, Basilisk, Oneiros, Scimitar) rather than a battleship. Their bonuses make them far superior for the remote repping and energy transfer roles. Rep ammount, range and cap stability will all be much better in a logistics cruiser than a battleship.
What you can do is employ the spider tanking principle, have every battleship in fleet fit one or more remote reppers. This can possibly be supported by adding a few logistics cruisers to the fleet as well. Any battleship with a good potential to armor tank can work for this, but some tend to work better than others. The Dominix and Typhoon are considered the best choices. They are balanced ships and can be fit for good dps with flexibility in range and good repping power. The Megathron and Armageddon are also good ships and can be set up for a lot of dps and decent repping. Other Amarr, Gallente or Minmatar bs can work as well.
The only ships that arguably should be avoided are the Caldari battleships. These ships lack the low slots to fit a decent armor buffer and while they can be used, they will be primary and they will go down fast.
My best advice is to play around in eft with different ships and see what works and what doesn't. A few tips:
- At least 1 or 2 remote armor repairers on each ship (Typhoon and Dominix can fit more)
- Don't fit cap recharger etc. Use cap boosters. Otherwise one neut will put you out of the fight.
- Use the lows for a good armor buffer/resist tank. Some ships can afford to use lows for gank, but tank should be the priority.
- Do not fit local armor repairers. Buffer and resists tank only. Your rep comes from your buddies.
- Concider a MWD or AB. If you're out of range of your buddies and get primaried, you'll die fast.
- ECCM is very useful. Jam resistance improves your collective tank.