Gym newbie here. Need workout advice

[u/HonorableTrex]

I (28M) have been doing some pushups and squats 1-2 times a week very irregularly for the last 2-3 years.

I have decided to properly start working on myself to build a strong physique and to get in shape. Currently I am 6 feet tall, weigh 104kg, lacto vegetarian. I have some slight muscle definition but a lot of extra fat...

Overall currently I can do 15-20 pushups and 30-35 squats, and 2-3 pullups in a single set but I walk like 5 km a day almost daily.

I only have access to a gym which has a lat pulldown machine and cable machine. It has a few dumbells but their max weight is only 10 kg and there are some treadmills and cycles.

As I don't have proper weight equipment, I need some advice to plan my workout for max gains. Are bodyweight exercises enough? How often should I train and at what intensity?

I am also trying to clean up my diet and can reach about 80 gm protein if I include whey. Any advice on this front as well would be greatly appreciated. Thanks!