I'd like to start a business in the service industry (not a restaurant) with a very low barrier to entry (as such I can't give specifics).
Aside from making the best product/service that I can, what can I do to keep customers coming back to me instead of new competitors, which I think will be a problem, considering the very low barrier to entry in my market? Are there any good books on this topic?
You can't have it both ways.
If there are low barriers to entry, there are low barriers to entry. It's easy for you to get in, and it's easy for competitors to pile in after you. However, there's a little more to say, because there's a difference between low barriers to entry in a broad market and raising barriers in the slice of the market you develop.
The two concepts you'll come across (though the language varies) are lock-in and lock-out. I'll illustrate them with examples from the cellphone industry.
Lock-in is where you make it hard for customers who value what you do to migrate away from you. Have you got a cellphone contract? Chances are you're locked in - you've agreed to take service for a minimum period, and your carrier is going to work hard to encourage you to renew (lock yourself in again) when the contract is getting near to term. You've bought a commodity, but you've accepted lock-in.
Lock-out is where you make it difficult for competitors to win your customers. For instance, prepay cellphone customers may be "earning credits" which will give them a discount on a handset upgrade. The customer isn't locked in - they can walk away. But a competitor addressing an informed customer of yours doesn't just have to show they have a better offer in general, but they may have to match the $50 credit. They're locked out - or at least, their acquisition cost is pushed up.
The best thing you can do is provide a better service than your competitors and it won't matter. You can't really force competition to stay out of the market, and if you could, you'd soon be in for a heap of anti-trust and anti-monopoly lawsuits, which you probably don't want either.
The reality is, competition justifies your whole existence. The fact that there is a whole category of businesses trying to do it means that (a) you have a viable idea, and (b) that the potential customer base will feel like "this is a thing that people are doing these days, so I should find a business that's doing it and get on board."
Granted, it means you'll have to have competitive pricing, and fight for customer's loyalty, but it is things like these that keep your business moving forward.
I'd suggest that instead of looking for how to prevent competition from popping up, that you focus on how to best attract potential customers' attention, provide the best service you can, and do it for a price that respects the customer's wallet. I know it sounds cliche, but if you stick with learning the tried and true principles of running a good business, you'll have more success than if you focus on making sure you're the only one on the market.