I would say toy cars, water play, shape sorters, stacking rings are all good at that age, but tbh at 13 months my ds went through a stage of totally losing interest in toys and only wanting to play with real stuff, mainly involving pulling everything out of cupboards, chucking the remote about, taking my phone etc.
Thankfully he started to get in to role play toys somewhere around 18 months which is so much more fun, so if you want to buy ahead favourites were:
Play kitchen
Happy land stuff from elc (esp. houses with doors to open and close)
Cleaning supplies - pretend hoover, dust pan and brush etc.
Train set
Little cars, helicopters, diggers etc. And rug with roads on
Dolls - pretending to feed them and put them to bed
Duplo building blocks
Balls - lots of different types soft ones, bouncy ones
Magnetic drawing board
Crayons
Tool set
Sand pit/water table
Got loads of this stuff second hand at baby sales so doesn't need to cost a bomb.
HTH