The most important thing I would suggest is monitoring how the statistics are maintained. Likely it's just the automatic update. Depending on the type of data, how it's stored in the indexes, etc., this may be grossly inadequate. You may need to do a full scan on your own on a regular basis.

As to the fragmentation of the indexes, unless you're running enterprise and can do an online rebuild of the indexes, I don't think you have much choice around that. Even a fragmented index can be helpful and fragmentation isn't always a big deal. Measure performance before and after a defrag to see exactly how much impact you might be suffering from.