National Electrical Code says that for general lighting and receptacle circuits, you can use 3 volt-amperes per square foot to calculate the load. However, the square footage is calculated from the outside dimensions of the floor area. So when calculating the area, don't forget to include the wall thickness.
National Electrical Code 2014
Chapter 2 Wiring and Protection
Article 220 Branch-Circuit Feeder, and Service Calculations
220.82 Dwelling Unit.
(B) General Loads. The general calculated load shall be not less than 100 percent of the first 10 kVA plus 40 percent of the remainder of the following loads:
(1) 33 volt-amperes/m2 or 3 volt-amperes/ft2 for general lighting and general-use receptacles. The floor area for each floor shall be calculated from the outside dimensions of the dwelling unit. The calculated floor area shall not include open porches, garages, or unused or unfinished spaces not adaptable for future use.
Let's say you're going to be servicing a 1300 square foot area with the panel, and it sounds like you're only planning for 120 volt general lighting and receptacle circuits. The load would be calculated as follows:
3 volt-amperes * 1300 sq.ft. = 3900 VA
3900 VA / 120 Volts = 32.5 amperes
In this scenario, you'd be able to use a 40 ampere double pole breaker in the main panel, and 8 AWG copper or 6 AWG aluminum conductors to feed the panel. However, you may want to leave room for future expansion, so the minimum might not be what you're looking for.
You may in fact want to use a 60 ampere double pole breaker, and 6 AWG copper or 4 AWG aluminum conductors. Even though you only need half that capacity, the cost difference might be worth it if you want the option for future expansion.
TL;DR -- find the breaker that shuts that red wire off, then slap the builder with it, so to speak
The builder of your house needs a slap with the NEC. There are two very clear Code violations here, and they're both things that are trivial to avoid.
First off, the lack of panel labeling isn't just a massive inconvenience to you, it's against Code -- the NEC requires it so that the next electrician/homeowner who looks at the panel can actually figure out what breaker to shut off to make a circuit safe or get that sparking oven to quit. In particular, it'd get dinged for busting 110.22(A):
110.22 Identification of Disconnecting Means.
(A) General. Each disconnecting means shall be legibly
marked to indicate its purpose unless located and arranged
so the purpose is evident. The marking shall be of sufficient
durability to withstand the environment involved.
and 408.4(A)
408.4 Field Identification Required.
(A) Circuit Directory or Circuit Identification. Every
circuit and circuit modification shall be legibly identified as
to its clear, evident, and specific purpose or use. The identification shall include an approved degree of detail that
allows each circuit to be distinguished from all others.
Spare positions that contain unused overcurrent devices or
switches shall be described accordingly. The identification
shall be included in a circuit directory that is located on the
face or inside of the panel door in the case of a panelboard
and at each switch or circuit breaker in a switchboard or
switchgear. No circuit shall be described in a manner that
depends on transient conditions of occupancy.
Second, what you have is indeed a Multi-Wire Branch Circuit (MWBC) -- the 52V on the black wire with breaker #23 OFF is stray capacitive coupling from the still-live red wire. The red wire, of course, is still live because of another Code violation, this time of 210.4(B):
(B) Disconnecting Means. Each multiwire branch circuit
shall be provided with a means that will simultaneously
disconnect all ungrounded conductors at the point where
the branch circuit originates.
So, it's time to find the breaker that turns off that darn red wire (leave #23 off while you do this!). Hopefully it will be adjacent to Breaker #23 -- in that case, you can get a handle-tie from the electrical supply house and handle-tie the two dodgy breakers together to fix the issue as per 240.15(B)(1). If the builder was as clueless as I fear though, that breaker is somewhere totally else in the panel -- something you'll want an electrician to fix.
Best Answer
Surface mount boxes and conduit are the usual. I don't believe you'd have to run conduit all the way back to the box if you terminate it properly.
You could also hang 2x4 lumber from the ceiling joists as a pseudo-wall, or simply plywood and attach wire and boxes to that.