You won't need a weighted vest to add on to your push ups to build strength, well at least till you reach the one arm push up and can do it for reps. Till then learn more about advance push up variants like diamond push ups, level push ups and so on. It would also help if you learn about how leverage works in calisthenics too cause even for normal push up can be made harder or easier.

If size is your goal your rep work out should be more similar to a bodybuilder which means rep range of somewhere between 6-18 per set. Stick to those ranges but keep in mind that you need to keep building on intensity too, so keep progressing to higher variants of push ups once you reach the rep limit. You could also consider doing this if chests are your priority: Wide arm push ups, when the get easier for you spread your arms wider, a few inches till it get easy for you (only spread further when you can reach the rep limit). Eventually, after a while of training like this, you arms will be almost like 'T' or a cross meaning that they will not having the full ROM as a normal push up because of this your triceps won't be getting much use. So do note that you'd still need to a normal progression to build up your triceps. Consider this form of push ups a supplement to your training.

Don't forget dips too. Horizontal dips are great but requires great amount of strength to do.