First off, you're going to need a reloading press. Lots of options here. I use a Forster COAX (with the LS jaws) but there are other choices that are dimensionally larger that will accommodate the longer length of the 338 and make it phyiscally easier to work with a long cartridge. RCBS makes a good one but the model name escapes me at the moment, someone will jump in with it I'm sure.
Next, dies. Redding competition seater and bushing FL sizer are a good choice. Forster makes good dies.
You'll need a bushing (.364 or .365 size for lapua brass. Oh yeah, you need to buy brass... (humor) just bite the bullet and buy lapua from the start (imo)
You're going to need a trimmer, boy, lot of choices here, Giraud is the best ($$$) but lesser trimmers get the job done
Hornady OAL Guage, bushing for .338 and bullet comparator and a good set of calipers, the more expensive the better
Bullet puller, hornady is good, get the proper sleeve for 338 for it
Powder thrower and scale, make it easy on yourself and buy an RCBS Chargemaster.
Reloading manual (s) recommend at least two
Loading block(s), 1 or 2 per caliber
Tumbler and media tons of choices here
Case lube, case polish
Media seperator, several choices here.
Maybe a case prep center, kinda depends how you decide to do your trimming, but the LYMAN prep center I like.
Powder (duh), the most common is RETUMBO or H1000 but many choices. RETUMBO is probably one of the safest to start with.
Primers, large FEDERAL MAGNUM MATCH is a good choice. Can be hard to find, so start now!
Bullets, lots of choices, Sierra 250 or 300 grainer are forgiving & easy to shoot. Same with Lapua SCENARS. Best overall all-around choice IMHO would be the Hornady 285 ELD however, later on after you get some "miles under your belt" with the process, you might consider moving up to solids like a flatline or cutting edge bullet. Expensive but will extend your range.
Having said all this, .338 is not a good caliber to start learning on IMO, I would suggest maybe a 223 or 308, a bit more forgiving. Starting with a caliber like 338 which can kill you if you mess up.... just doesnt sit well with me. You don't just jump into this that easily, there's a pretty decent learning curve here . Most of us have been reloading for years if not decades and are still learning. Best bet is to pair up with somebody to show you the ropes in person. Try to do that if at all possible. Maybe somebody from your club, ask people, get to know people there. BUT FIRST, read the "stickies" here on the Hide that cover the basics of reloading and gear. The above list is not all inclusive and alot depends on preferences that you develop over time. By the time you add up the cost of components above for a $$ hit all at once, you may well decide to stick with factory loads for awhile, lol, it's alot to start with! General rules; BE CAREFUL, start low and work your loads up SLOWLY, don't get inpatient and "try & run with the big boys" from the getgo! Lots of good advice here on the Hide, ask frequently and don't be afraid of dumb questions, there aren't any if you're just starting the reloading game. A mistake with a cartridge that big can take your face off or worse. Take your time, LOTS to learn. Did I mention maybe starting with a smaller cartridge during the learning process.........???