No jumping and reselect last selection

[masell]

Makes * search of visual selection not jump.
Re-selects your visual selection with gv so you can change it more easy.
Sets hls so you see the matches.

[ngtinsmith]

Can confirm, this prevents the selection from jumping.

Another small adjustment would be to return to NORMAL mode from VISUAL mode so manually jumping (n / N) will not select the content in-between the jump range.

xnoremap * :<C-u>call <SID>VSetSearch('/')<CR>:set hls<CR>gv<Esc>

Edit: Scratch that, just omit gv to not enter VISUAL mode, no need to pipe <Esc> (my preference)