It depends how much you're willing to spend. The one mattkc linked (which isn't in stock at amazon but is available on aliexpress) is actually decent value primarily because it also serves the purpose of a hot air station as well all for 100$. Some of if not the best soldering stations are made by hakko and for hot air stations by quick. Louis Rossmann the tech repair god uses them. You can do the job with cheaper stuff but it is going to be more of a hassle.

The HAKO FX-951 240$
The Quick 861DW hot air rework station is 290$

Obviously they're really expensive so given that you're a beginner the Yihua 872BD+ or similar which can be found on aliexpress for around 100-120$ should be good and should last you a while before you'd even consider upgrading. Obviously this assummes that you're going to use it for other repairs and projects in the future and not just for a one-off repair.

What I also recommend is practicing soldering before going in and doing the job since the pins of the HDMI ports are really small so it's best to avoid any kind misplacement or bridging of the pins due to too much solder.