I've lived with ONLY FA31 Ltd for over two years, using it for all sorts of shooting. And it has served me well. Here are a few modest examples:
So I used only one lens for everything. My dad, on the other hand, needs to have everything covered, from wide for crammed spaces to super tele for birding.
So it depends on your shooting style, if you need various FLs, you can start with the previously recommended Sigma 17-50 as a general lens, and then gradually add in primes for FLs that you most shoot at. FA31 would be my first choice for a 50 equivalent. Sigma 30 is also nice but I don't like its bulk.
For a 35 equivalent, DA21 is great, but I'd skip that and go for something a bit wider, a DA15. You can have a lot of fun with that lens. It's great for shooting into the sun and comes in handy for landscapes and crammed spaces. I own it and love it.
I also have the 43Ltd that others have mentioned, but I find it's FL a bit unusual and don't use it much. I read a few similar comments from other people on this forum, so before you decide to buy DA40 of FA43 I'd recommend you set your general-purpose zoom to about 40mm and leave it there for at least a week or two. If you find it pleasing to your eye after using it for a certain period of time, only then buy a lens with that FL.