Linen doesn't have much elasticity and it prefers a humid climate. If you live in an arid climate, you might want to try weaving with a cotton warp and the linen as weft, just to see how you like it. It does take some careful handling as warp, but beaming under tension using a warping valet will help. :) I'm sure others will have some more hints and tips.
Yes you can just wind directly onto the beam. Make sure the threads don't get hung up on the pegs. Beam with tension. You won't need warp packing if you do beam with tension.