A couple of common lifting issues include:
1). The layer below has to be completely bone dry (with hairdryer-or at least a three hours air drying) before glazing the next layer. If it is slightly damp it can still lift.
2). Going over the first layer gently with no pressure on the brush so not to agitate the underneath layer.
3), Leave 2nd wash alone once it is down and try to avoid temptation to fuss with it -as going back in again can re-lift layers below.
4). Knowing which pigments lift and which stain is helpful. Staining pigments are easier to glaze with eg, Phthalo colors, quinacridone colors, (test your pigments-lay down a small wash and then see how well they lift after stroking 3 times with a damp brush (be consistent in your testing). Non-staining pigments are usually granulating eg Ultramarine blue, manganese blue and lift back to white paper. (To save money manufacturers of student paints often use a mixture of colors eg. cobalt blue may contain both phthalo blue and ultramarine blue
6). Some student grade watercolor papers aren't absorbant enough and paint just floats on surface-and lifts way to easily. Try this: http://www.cheapjoes.com/arches-watercolor-pad-140-lb-cold-pressed-9-x-12.html ($10.90). IMO, quality of the paper is more important than the quality of paint. I think you'll enjoy layering (without lifting) on this paper with the paints you already own.