There are three main problems in personal robotics:
1) The power/weight/cost triangle for actuators.
2) Battery longevity.
3) AI or other user interfaces that actually make sense to people.
All of those are open research problems.
That being said, if you want to prototype, you can start with an Arduino, because it is very easy to get started with, but it will very quickly become limited. If you want to do things like smart navigation in realistic indoor environments, you will need a lot more computational power (think chair legs, table cloths, vacuum cleaner left on the floor, lamp cables across walkways, ...) Thus, something like an Intel NUC or a mini-ITX motherboard with a real Intel CPU on it would be more suitable for the high-level control. (The Arduino can still do the low-leve bit banging to send control signals to motors/actuators and read raw sensors.)
Education is always good. If you can get a MS Robotics, you'd probably enjoy it, and it might just be a good investment for you in general. However, if you're currently running a business that's providing a living for you and a family, the culture shock of back-to-school might be very harsh.
In general, the "personal robotics" problem is much easier to solve when the domain is well defined. Think Roomba for vacuuming, or RoboMower for lawn mowing. Because the task is well defined and the environment is well defined, safety, runtime, robustness, cost, and other important factors can all be selected to create a product that would actually be bought by people (they provide enough value that the price is worth it.)