For YouTube you will want a GPU that supports the latest video codecs. YT is currently using AV1 and VP9.
The cheapest card with hardware AV1 decoding is the Intel ARC A310. However, for optimal operation it requires Resizable BAR, a feature which your i7-3770 system does not support. The cheapest AV1 card from AMD is the RX6600, and from Nvidia the RTX3050.
If you're on a tight budget, you could forgo the AV1 codec and get a card with only VP9 hardware acceleration. In that case the GeForce GT1030 GDDR5 offers good value for money.
That said, your CPU should be powerful enough to decode VP9 streams up to 4K60 without any assistance from the video card.