Trailer movement consists of movement in 3 directions - fore/aft, vertical and side to side Some kind of chocks will take care of most of the fore/aft movement. Jack stands at each of the four corners plus another set of jack stands or bottle jacks ahead of the axles will greatly reduce the vertical movement. JT Strongarm, BAL Lock Arm or Ultra-Fab Eliminator cross bracing/struts will greatly reduce the left/right movement and can be used in the fore/aft direction too.
Vertical movement will depend somewhat on the strength of the frame and it's length. For a longer TT, definitely use jacks next to the axles. Scissor jacks work better than electric "stabilizer" jacks for movement. Camco makes lightweight stacking jack stands for trailers.
Some get used to movement and some don't like it. It bothers me but not much with DW. We have elec. stab. jacks and cross bracing is on my wish list.