for conner being 4 months, the things you can look out for are:
reaching out to try knock toys (while under the baby gym) - he may not actually grab the toy, but he should try reach out and knock them - if he does grab them - clever boy!
watching you as you walk around. his eyes should be able to follow you or if you are talking, he should be able to look around until he finds you
pulling to sit - good head control and an effort from him - like he is also trying to sit forward with your help
bearing weight on his legs while you hold him in a standing position
and things you can start stimulating for from 5 months (or even now if you feel he is ready):
sitting. when you prop with pillows, if the pillows are literally all the way up his back, this is fine. but if you are literally sitting him on the floor with just one pillow on the side and behind, his back may not be strong enough yet to not fall over (best to start this from 5 months) so for now, prop pillows high to keep him in the sitting position
you can start rolling him over. around 4-6 months baby learn to roll over by themselves. so hold his legs (while he's on his back) and roll him side to side to stimulate that feeling. then roll him onto his tummy, leave him for a couple of minutes, and roll back onto his back.
start telling him what things are. like:
look in a mirror and say "mommy. connor." and point at who ever you are telling him it is.
tell him, now you are drinking your bottle, now we are bathing, when you put the vest on and push the poppers at the bottom, count "1,2,3"