A Lee case trimmer for each cartridge you plan to reload.
Forget what others may say about never having to trim .38 Special cases. Yes, you do, if only to get consistent crimps on the bullet. But over time, .38 Special cases will stretch, depending upon how much pressure they've been subjected to, and will need trimming.
After trimming, you'll need to chamfer the case to remove burrs. The Lee chamfer is good. Inexpensive too.
A block of some kind to hold the cases upright, while processing, is needed. I like the MTM Case Gard block, but Hornady makes a good one too. You may wish to buy two, so you can move from one block to another as you process cases. For example, after charging the primed case with powder, place it in a separate block. This helps prevent double-charging.
A small penlight, to look down into the cases to look for double charges, is handy.
If you're not using carbide dies, you'll need case lubricant.
Calipers. This will save you a lot of guesswork and mystery. The manual ones are good. An electronic one is easier to read. Ensure either is a name brand, so it's accurate.
The best manual is made by Lyman, in my estimation. Lee makes a decent manual, but the Lyman covers all aspects well, and with plenty of illustrations to accompany the information. The latest version is No. 49. It's worth the money.
You'll want a means to clean the crud off cases, after returning from the range and before reloading. A rag dampened with lighter fluid will remove fouling, bullet lubricant, crud, dirt, etc. But you'll probably want a vibratory cleaner eventually. I like my Hornady but any well known brand is good. You can reduce their noise on a hard floor by putting them on a small rug. This won't affect their vibratory operation and is much quieter.
The original factory ammo box may be fine, or it may be flimsy. You may wish to go to plastic boxes made for reloads, such as those made by MTM, Dillon or others. They're sturdy and will keep ammo protected from dust.
Labels. Absolutely, do not forget to label each box as to the case manufacturer, primer, bullet, powder, powder charge, date of reloading, expected velocity (according to your manual), etc.
Buy the kind of cartridge box that doesn't have a removeable lid, and tape your label to the exterior of the box. Otherwise, you may accidentally switch lids and misidentify a load.
Notebook. Write your load in this book as well, along with the info, and then take it to the range. At the range, you can take notes on how well it performs. This will save you a great deal of mystery, trial and error down the road. Don't forget to note which gun you shot your loads in. Each gun is an individual. One will like a load that the other dislikes.
You'll find other doodads and gadgets down the road that you need, but this will get you started.
I cranked out my first reload in 1971, for a Model 94 Winchester in .32 Winchester Special I still have. I used a Lee Loader. Today, I reload for nearly 25 different calibers, using a Dillon 550B press for high volume, and a Lee single-stage press for the occasional box or two or little-used calibers.