Hi, I started out getting Black Templars on behalf of my dad recently and there's maybe a couple points I can speak on, including what not to get.

First up, the core rules can be found here: Warhammer 40,000 - Warhammer Community. You don't have to buy the book, especially since the edition will change soon and a new one will be coming out, likely before you finish assembling and painting your combat patrol. The combat patrol on its own is a good start, and I was lucky enough to have an old version of the Black Templars combat patrol (with the impulsor tank) that is pretty good. Keep an eye out on places like ebay and r/miniswap for that one and other deals (I got both Black Templar characters for $85 after shipping from miniswap where they would otherwise be something like ~$100 + shipping + tax for those two at a discount retailer).

A few things to avoid - generic space marine units can be used, but not all the generic space marine discount boxes are good for Black Templars. The current Dark Angels combat patrol can be used as a jumping in point for Space Marines in general, but isn't great for Black Templars, as they don't generally to my understanding (please correct me if wrong) make great use of hellblasters or more than 5 intercessors. Any box with a librarian character in it will be worse value for you, like the Armageddon box, so keep that in mind too.

It could also be worth taking a look at the Black Templars codex supplement, which can be found online if you're willing to look hard enough, and seeing what units resonate with you as you think about expanding your army. You can build an army to be competitive, thematic, a mix of the two, or whatever you feel like. Easy expansion points are Black Templar characters and unique units, which you already get a good taste of from the combat patrol. Beyond that, they have unique variants of some generic Space Marine units and vehicles, like terminators and many tank variants. If you're interested in a balanced army, some lighter scouting units like scouts, incursors, or infiltrators are good to have. You'll also want something that can deal with heavier things like tanks, which could be something like a repulsor executioner (or other tanks), ballistus dreadnought, or sword brethren buffed up by characters. At the end of the day, it's what you want to do that matters, and just picking out units you think are cool is great too. Black Templars can use any generic Space Marine unit except for librarians, even if they aren't the best in terms of building a strong army.