Ed- Keeping the game interesting to you is more important then specific setups, but since you asked how I would do it 
First off, being in a small corp is much better then going solo. Other then the social aspects, there's limits to what 1 person can do, even with multiple accounts. If your in a corp where most players have multiple accounts, that's a bonus too!
It really all boils down to how much play time you have and how much multi-tasking you can do. And how effcient you want to be with your characters.
If you just want the flexability to go out and do different parts of the game, then Miner/Harvester, Combat/PVP, and Production/Marketer are the ways to go. Dedicated, you'll be very good at each of these parts of the game as your charaters progress and have fun doing it.
The complication comes if your looking to integrate the (3) accounts to maximize the return of your online time.
By far the easiest way is to just have three dedicated miners. The activites are localized, meaning that your attention is more focused, and you don't have to be too snappy on the alt-tabbing. It's also very lucrative.
Next would be having (3) industrial charaters, dedicated to Factory/Prototype/Marketing. You'll spend most of your time buying and transporting raw goods and produced goods, analyzing the market, and working on spread sheets. But you'll be very competitive very quickly - the PT/RE character will lag a little behind. You'll also spend a lot of time in chat, since you'll need to deal personally with people for things not on the market.
Last, you could do (3) charaters for farming. 2 combat and 1 support. This takes a lot of alt-tabbing and focus for your entire game time, but you'll earn alot of NIC.
When you start mixing, you're going to get less effect from each group. You simply can't work spreadsheets and view market data while your in combat, but you can mine, but you risk getting roamed on and you have to back out of combat occasionally to move the miner around. End result is you'll be less effienct in both.
Personally, I play for the variety, and not the effciency. I don't mind having my miner bot in a transport just idling while I combat, or if my production lines are running continually, and lastly having my combat tune sit on the can while I mine.
For me, if I was to start 3 new bots, I would go 1 mostly miner with some combat support (remote rep), Laser combat bot with enough to mine with termis (so you can have 2 miners going) and a production/marketer that can at least drive a seq. Keeping the bots in the same activites at the same time (all mining, all combat) is just simpler to manage. And you have time with dual mining to do spreadsheets and market research.
