best compute power (total computational power) = ryzen 3 > i3 > g4560
best clock GHz (for small games / single and dual core games) = i3 > g4560 > ryzen 3
ryzen will be more pricey when you add the RAM as it requires a matched pair and higher (2400+ and some/most suggest 3000) mHz
intel cpus less fussy over RAM clock speeds, and can settle easily for 2133 mHz (a lot cheaper than 3000 for sure).
so when you look at budget, ensure you look at everything, not just the cpu.
browsing is windows which takes generally 2 cores and some multithreading = intel cpus with higher GHz
dota is a 2 core game = intel cpus with higher GHz
overwatch is a multicore + multi thread game = ryzen with more cores and threads.