What is "length of pull"?
The distance from the rear of the buttstock to the trigger. For most people this also corresponds to the distance from the inside of the elbow to the tip of the trigger finger.
What rate of twist should I go with for a .270?
This depends on the bullet weight that you intend to use. A tighter twist is necessary for heavier bullets. Talk to the guys at HS Precision. Tell them how far out you plan to shoot with this, and what you plan to shoot. Leave the twist rate up to them.
What rings/base setup?
There are plenty of good brands out there, but Badger Ordinance seems to be the unanimous king of rings and bases. They charge accordingly for them. Ask HS Precision what they recommend.
You're smart to do some research beforehand, but don't hesitate to pose these questions to your builder before you give them approval.
This is a custom, so get some custom features added to it. Think about what you love about your current rifle and be sure it is added to the new one, and see if anything you hate about your current rifle can be corrected in the new one. Or heck, just go for looks: get a barrel contour so big it looks like you have a suppressor on there, have the barrel fluted, have the stock done in some custom color or pattern. Make it yours.
Good luck!