Prime lenses are great.
They are usually better (optically) than all but the best zoom lenses...and primes are less expensive. Also, they are usually faster (wider max. aperture) which is probably the best thing about them.
A good thing about prime lenses, is that they can force you to move around more, which helps you to think about your composition and perspective...rather than just standing in one spot and zooming your lens.
(on full frame), 50mm is "normal" view so that might be a good first lens. The 50mm F1.8 is so cheap that no EOS owner should be without it. The 50mm F1.4 is a little better but much more expensive.
For portraits, a lot of photographers like a lens that is twice normal. So 100mm would be something to look at. Canon has a 100mm F2.8 macro lens that I've heard is a also a good portrait lens. That might be a good option for you.
On the other hand, zooms can be convinient...which may be better for a first lens. The companion lens for the 5D is the 24-105 F4 L...supossedly a very good lens. (all 'L' lenses are pretty good).
Another talked about 'everyday' lens is the 28-135 f/3.5-5.6 IS. It's a nice focal range and IS (image stabilization) can help you get shaper shots at lower shutter speeds while shooting hand held.