The child is one year old. At this stage it's learning from everything around it. Try to give the child different (but safe) objects and see what they gets engrossed in without trying to push them in a particular direction and take it from there.
For example, different coloured clothes, dolls, moving objects like cars, building blocks. They don't even have to be "toys", just any objects that pique the imagination. Remember that everything is new and educative at this stage.
Regarding play. Touch, hold and cuddle your child as much as you can till the age of 5. This is known to have psychological and mental benefits going forward. The same applies to rough and tumble play (safely) in parks and indoor playgrounds or even in the house. The bonding benefits are immense too.
If the weather permits, allow the child to go out and play with them. A ball or wheelable vehicle would help.
At this age kids generally don't play with other kids, but indulge in parallel play, so don't worry too much about that aspect.
Lastly, rather than expensive toys, give the child your time, become a child while playing with the child.