I walked from Carlyle to near Housesteads in April (I then turned north on the Pennine Way) and I remember passing by Brampton. I've just had a look at the free OS map on Bing Maps and the walk from the station to the wall looks to me to be straightforward enough. Once on the wall, of course, I found it easy to camp, bunk, etc. I came off the wall once via a direct footpath to a campsite near the Twice Brewed pub and stayed the night in campsite bunkhouse which was very nice, I had a 4 bed room to myself. I then ate at the Twice Brewed pub which was pretty good as well.
I then rejoined the wall walk the following morning, not far away at all. I've never walked beyond Housesteads but I assume its straightforward and it doesn't look difficult to get to Wylam station when you leave the wall.
Unless those with experience of the route from Housesteads to Wylam know differently I'm sure that for walking demand and being able to see the best bits, hiking from Bramton to Wylam is the best section.