You dont really need a good gpu to play league of legends. League of legends is more cpu heavy than cpu. But one of the most popular budget GPUs for gaming is the NVIDIA GeForce GTX 1650. It's a capable GPU that can handle games like League of Legends with ease. It offers a good balance of performance and affordability. Additionally, AMD's Radeon RX 5500 XT is another option worth considering in the budget segment.