For 357 Sig, I've got Redding, RCBS and Dillon Carbide dies. I use them all for different things. The Dillon dies are expensive, and they don't size down on the case as far as the others, due to the belling of the die mouth to facilitate the progressive machines. Each manufacturer has something about their dies that are better in one area, or another.
As for lubing the brass, I've found that it's much easier on the brass to spray it lightly with One Shot, or Midway spray lube, or any of the other spray lubes. I just tumble the sized brass in untreated corn cob for about 20 minutes to take all the lube off.
Since you've never loaded this round before, be aware that even though everything you read says the round headspaces off the case mouth, there are actually two datum points with this cartridge. First is the case mouth, and second is the shoulder. Even if the length of the case is correct, if the shoulder isn't set back far enough, the loaded round won't chamber completely. When you set up your sizing die, be sure to try the sized case in your chamber to see if the slide will go all the way closed. This is where a lot of people have trouble with bottleneck pistol cartridges, so just make sure you set the die up correctly.
If the die won't go down on the shellholder far enough, it may be necessary to mill a few thousandths off the shellholder to allow the die to go down farther. Another way is if you have several shellholders for the same caliber, measure the distance from the inside of the shellholder, where the base of the case sets, to the top of the shellholder, where the die contacts. You'll find that almost all shellholders vary in this measurement, even from the same manufacturer, and you may have one that is "shorter" in this area.
I would recommend that you get a separate crimping die, as this round has a very short neck and the bullet needs to be securely crimped in place to avoid setback. It's a high pressure pistol cartridge, and you need to prevent things that will increase that pressure.
Another thing is the bullet itself. You can't use just any 9mm bullet for 357 Sig. Due to the short neck of the case, the bullet needs a straight bearing surface for the neck. It also needs to be either a flatpoint or hollowpoint bullet. Most roundnose bullets won't work, especially any with the NATO design, which has a long ogive. Remington Golden Sabre bullets also won't work, due to the stepped design of the bearing surface.
Once you get your gun and dies, and get things set up, there are quite a few people here who can walk you through any problems you may encounter.
This is enough information for now, but if you have any further questions, don't hesitate to ask.
Hope this helps.
Fred