Just realize that the path can be addictive and costly but there are great rewards to be had. Just picture turning something nice for your wife / kids with some of the cool wood that you have collected. Or teaching your children to make a pen they could use at school when they are older.
I have a preference for chucks from VicMarc and OneWay. I also have one from Nova which works perfectly well but seldom use it.
Thompson, Dway, Carter, Robust are all suppliers of quality tools. You don't need them all at once and can acquire what you need over a long period of time. Learn to sharpen & use the HSS ones that you have while you learn, add the quality pieces as your skills improve.
There are cheaper products for all of the above that originate in China. Some people use them and have good luck with them. I try to avoid that and use tooling from those mentioned above.
Don't ignore the used market. Many have purchased a lathe and all of the tooling only to never use it very much. It sits in the shop / garage taking up space until they put it up for sale for a big discount. There is always a good deal to be found out there.
Ryan, we've followed along with your wood purchases,.....2-3 weeks of your wood acquisition budget would bring the lathe, tooling, grinder, & CBN wheels home.
@Big Ry