I'll second the DA17-70; complement it with a DA(L)35/2.4 (not the limited) for low light conditions and you have something that will serve you well for a long time.
This will leave you some money that can go towards spare memory cards (don't put all your eggs in one basket), a camera bag, some goodies for maintenance (lens cleaning stuff, blower, ...), a tripod and a 'simple' flash.
If funds permit it, you can replace the DA(L)35/2.4 with the Sigma 30/1.4.
That's the short version of the story
Starting with primes is nice. But the selection of primes is highly depending on the needs and a highly personal one.
The way I visualize Egypt (never been there and haven't done research on it), it's vistas, pyramids, street shots and some indoor work (entertainment, musea). In which case I would start with the DA21Ltd. I think that that lens can live most of the time on my camera during the trip; but I might be wrong.
A 40mm or 50mm will nicely complement the 21mm on the trip; even 70mm might do. 70mm gives me the option to zoom in a little on details, 50mm and 40mm less so.
So lets assume you've opted for 21mm and 70mm (OK, the combo is a little outside the budget but that's not the point now) and they have served you well during the trip. When you're at home, your circumstances change. You've already found that 70mm is too long for most indoor shots (and 50mm will be as well in my opinion) and now at home you find that 21mm is too wide for your liking most of the time; you're always cropping in post processing or feel that you're always pushing the camera in the face of people when you use that lens.
There comes prime number 3; something in between 21mm and 70mm
In short, I think that you (for now) are better off with a standard zoom as your main lens and a standard prime for low light work. The prime can, at a later stage, be the base for a different kit if you feel that need.