I'm a one-man company, and a couple of months ago I shipped version 1.0 of my product after a year of beta testing. So far it has been successful; the product is selling and the customer base is growing, which is fantastic.
I manage my backlog publicly using Trello, so people can see the backlog of ideas, the current sprint, and what has been completed. Every morning, I wake up, check my email, and there are five new suggestions for features/changes to the product. I'm lucky to complete one or two per day, so the backlog is growing faster than I can get through it.
The suggestions range from:
All of these are important, and I feel very lucky that so many people are suggesting ways to improve the product. But managing the suggestions is becoming difficult. During the beta process, I had a forum for people to make suggestions, and I added them to the backlog so people could track the suggestion. That process seemed to work well when the number of suggestions wasn't too high. Now, I feel like I'm drinking from a fire hose.
Hide the "wish list" from public eyes. This is for your eyes only. No need for competitors to be able to latch onto your feed of good ideas from your own customers. Furthermore - it creates expectations of implementation for every item there that you do not have the capacity to fulfill. Treat the input from your users as a raw list from which you pick-and-choose items to build roadmaps. Roadmaps can be published once you finalize them.
Also, It is not written in stone that you have to implement every idea you get, even good ones, in the order you got them. You should use the ideas as input and assign priority to ideas based on how good you think they are, how urgent they are to your growth and also how much an idea weighs (one requestor? two? twenty?).
So, to sum it up
It's great that you're getting so much feedback from your users. Getting feature suggestions is a good indicator that customers care for your product. Congratulations :-)
In reply to your questions:
Ok, so why did I highlight innovation management in the above paragraph? Well, that's exactly what you have a problem with right now. Your old process has served you well, but now it's time to change it. There's no reason to do anything fancy with crazy scoring models and the like, you should keep it small and simple. But you need to be clear on this. Here's a few tips from the top of my head.
I read this post once by a famous startup (37 signals, I think - but not sure).
They had a similar problem in which they were barraged with feature requests - and the way they handled it was to just forget about it until a particular request was being repeatedly asked multiple times.
I think making the list private and replying with a simple "thanks! I've put it in the queue" should be good and you can put a +1 everytime a similar request is made.
Once a feature has reached a particular threshold of +1s, it could go into the actual implementation queue.
However, you must realise that many times, users will send a feature request and not really care about if it is really important to them or how much time it would take the developers to implement something. So its just best to prioritize things and understand that some of those features will never make it to the final product.
Many congratulations on your successful product!