Great advice so far. I'd suggest you approach this much like you did fly/jig tying and trap maintenance. It's a part of the process, and a valuable one, and most of us find we enjoy the act of reloading very much. For me it's very relaxing.
I'll suggest you start with a good kit. I started with an RCBS kit now 25yrs ago, and have added some other gear along the way, but really everything is still going strong after 25yrs of use, several moves, and plenty of loading. The big names are all pretty good, and if I were starting out today I'd strongly consider which of the RCBS/Lyman/Hornady/Redding kits was on sale as a great starting point. I like my RCBS Trim Pro 2 (which Chris already gave a sterling recommendation), and I like my Hornady powder measure (which is great for pistol rounds but I don't use as much now that I'm primarily loading rifle rounds). I have the Midway stainless dial caliper, and as long as I can keep my son from stealing it from me, I see no reason to replace it, ever, until it breaks. A good tumbler or ultrasonic cleaner would be a nice add-on in the short term, as well, as clean cases make for more consistent ignition and are easier on dies in the long run.
As for dies, I like Hornady New Dimension dies. I try to get them for all the cartridges I load. I've had three sets of Redding dies, and two of the three have had QC issues, so I'm not a huge fan. I have some Lee dies, but again, I see the difference in quality and for the $10 difference in cost, I'm good with Hornady. I've also used RCBS and Lyman dies to good effect, and still have a bunch of RCBS pistol dies around. If you start really chasing precision, a good neck die will be a welcome addition. I use Hornady neck dies because they're not cartridge specific, and I can use the same .308cal neck die for 308Win, 30-06, 300WinMag, and 300Wby. I like easy and cheap, and that's both. One other die I'd suggest is an inexpensive universal decapping die, as it makes for quick decapping of multiple cartridges in one sitting, without having to swap dies around. It works well for me since I decap, clean, resize, and the regular dies decap and resize in the same step.
Now, what I'll add is to get some good hand tools. Initially, you'll be doing most of the work by hand, so a nice set of RCBS or Lyman hand tools will make that easier. I like the VLD chamfer tool I have from Lyman, but I'd certainly like the one from RCBS, too. I also have primer pocket cleaners from RCBS, and I have a nifty little tool for getting tumbler media out of the flash hole which came from Lyman. I don't see it often on store shelves, but it's easily one of my most used tools. Here's a link to it:
https://www.midsouthshooterssupply.com/item/000157777750/flash-hole-cleanerNote, too, that Midsouth has the Lyman Crusher kit for about $235 right now.
I suggest you spend some time reading the Hornady Ballistics Resource online:
http://www.hornady.com/ballistics-resourceIt's one of the best treatises on what happens inside and outside the firearm when a cartridge is fired. Check out RCBS videos on the steps of reloading, for a basic overview, as well.
Much of the data out there now for Weatherby rounds is pretty watered down, so I'd suggest Nosler and Hodgdon as good starting points (though even some of the Hodgdon data is dismal), and Barnes for their bullets.
Good luck and keep asking questions! When you take the first game animal with your own loads, it's a new kind of good feeling.