Would my Lighting diagram work?
Wiring

This is what your wiring diagram should look like.



Notice the black wire is used to feed the switch, while the white wire is markered and used to feed the light from the switch.  This is because the black wire going to the switch will always be hot, but the white wire "returning" from the switch is only hot when the switch is in the ON position. The white "switched" wire can be marked simply by wrapping a bit of black electrical tape at each end of the wire.

All the grounding conductors are tied together, and connected to the box (if a metal box is used).

Box Fill Calculations

According to section 314.16 of the National Electrical Code (NEC), you'll have to count each conductor that enters the box once, all the grounds as one, any luminaire studs, hickeys, or fixture straps as one, each single yoke device is 2, and internal clamps are 1. Once you have this number, you'll multiply it by the value in Table 314.16(B) according to the largest conductor used. This will give you the total minimum box size, in cubic inches (cubic centimeters).

Ceiling Fixture Boxes

For each ceiling fixture box (excluding the last), the box fill will be as follows:


3 12/2 cables connected to box = 6 (13.5cu.in.).
All grounding conductors = 1 (2.25cu.in).
A luminaire stud, hickey or strap (to support the light) = 1 (2.25cu.in.).
Fixture wires less than 14 AWG = 0 (see 314.16(B)(1)ex 1.).
Total Box Fill = 8 (18cu.in.).


Assuming you'll be using 12 AWG wires, Table 314.16(A) tells us you'll need a 4" x 2 1/8" round/octagonal box for the first 3 boxes (or a box at least 18 cubic inches).



The last fixture box fill will be as follows:  


2 12/2 cables connected to box = 4 (9cu.in.).
All grounding conductors = 1 (2.25cu.in).
A luminaire stud, hickey or strap (to support the light) = 1 (2.25cu.in).
Fixture wires less than 14 AWG = 0 (see 314.16(B)(1)ex 1.).
Total Box Fill = 6 (13.5cu.in.).


So you'll need at least a 4" x 1 1/2" round/octagonal box, for the last box.



Switch Boxes


1 12/2 cable connected to box = 2 (4.5cu.in.).
All grounding conductors = 1 (2.25cu.in.).
Switch = 2 (4.5cu.in.).
Total Box Fill = 5 (11.25cu.in.).


This means you'll be able to use any device box larger than 11.25 cubic inches, for the switches.



Final Diagram



While 12 AWG wire may be a bit overkill for this installation; if that's the size wire you have, there is no problems using it.

According to section 300.15 of the National Electrical Code, all junctions must be made in a box or conduit body. Section 314.29, adds that the box must be "accessible without removing any part of the building".