You will need to fit a main breaker right at the meter, either by switching to a meter pan with integral main breaker, or by putting a main breaker where the former panel was.
The reason is the wiring run from the meter to the main breaker is unprotected - it has no overcurrent protection. It's one thing when it simply comes 2 feet straight through the wall. But it's quite another when it travels through locations not normally associated with electrical service - many more spots for a careless workman to drive a nail through it, and the workman would not be on guard for that since he wouldn't be working right at the panel.
With a new main breaker installed, your wiring to the "main" panel would be a new run with new cabled. You would also run 4 wires and keep grounds and neutrals separate in the new "main" panel, since technically the main breaker at the meter is the official main panel, and this is technically a sub.
As far as the branch circuits, this is fairly easy work. Ask the electrical supply for advice, but you'd need boxes (I like metal) that give you enough space to make the splices. Take a simple #14 branch circuit. 3 wires would come into the box, 3 wires would go out. The hots and neutrals get spliced to each other via wire nuts etc. The grounds could be handled the same way or be clumped into a bunch with other circuits from that same new panel.
Every box must have enough cubic inches to meet the rules. Here's how you calculate those:
Each wire size has a cubic inch size associated with it. #14 is 2.0 c.i. #12 is 2.25 c.i. #10 is 2.5 c.i. Etc.
- find the largest ground wire in the box. Based on that size allocate X cubic inches for that one ground wire. All other grounds are free.
- find the largest wire in the box that has a cable clamp. Based on that size, allocate X cubic inches for that cable clamp. All other cable clamps are free.
- For each other wire, allocate X cubic inches per wire based on its size.
- If you stick a receptacle, switch etc. on the box, each receptacle costs 2 * X cubic inches based on the largest wire going to a receptacle.
Take a box in which you are splicing four #14 circuits. 4 cables in, 4 cables out; 16 wires plus all the grounds. The cost is 16x2.0=32 cubic inches for the wires, 2 cubic inches for all the grounds, and 2 cubic inches for all the cable clamps. Total 36 c.i.
Mark your wires obsessively. They make 10 colors of electrical tape, and would probably end up doubling up, giving 55 combinations (not 100; you can't distinguish brown-blue from blue-brown). The resistor color code is a good way to turn colors into numbers, see also the AT&T phone color codes. In cable you cannot mark white with a color other than white or gray, or you will accidentally designate it as a hot. Don't do that. Doesn't apply to individual white wires in conduit. That doesn't apply to individual white/gray wires in conduit.
One slick installation is to carry all the circuits to the new box in conduit. A few things on that. First, do not clump them all into one huge conduit. Unless you are willing to significantly up-size the wire, there should be no more than 3 circuits per conduit - 4 circuits is permissible if all of them are #12 or #14. This necessitates a spread of parallel conduits - quite an impressive sight. If wire is larger than #8, watch your derate rules very carefully so you don't have to upsize the wire.
Use individual THHN wires, don't stuff cable into conduit. They make 11 colors of THHN wire, but black and white will suffice. Neutrals must be white or gray. Hots must be natively another color (not green), no remarking allowed. Blue and green tape on a white wire makes it the neutral from blue-green circuit. It's super important to keep your pairs matched up.
You can only fit 9 or sometimes 10 wires in 1/2" conduit. With 3/4" or larger conduit you will hit the 4-circuit limit before you run out of wire space. Metal conduit serves as the ground wire, so 4 circuits is possible in 1/2" conduit.