Depends also if you are going to work at a permanent station or if you are going to go contracting. If you´ll have to fly often you´ll try to keep your toolkit small to prevent from having to pay excess baggage fees.
In Europe in many countries the company has to provide the tools due to better accountability. I would leave out any tools which are aircraft specific or would need to be calibrated. You´ll get them usualy in the tool crib.
For me a basic set would be:
1 set of straight edge screwdrivers 2mm - 12 mm edge
Phillips 1, 2 and 3
Phillips 1 and 2 carburetor (short and stubby)
Straight edge screwdriver 8 mm stubby
Angled screwdriver straight edge 8mm
Angled screwdriver Phillips 1 and 2
Bitholder screwdriver (Snap-on makes the best)
Set of combination wrenches AF
3/16 to 1 1/4 inches
Set of openend wrenches AF
1/4 to 1 1/4 inches
1/4 drive ratchet
extensions 1/4 drive 2", 3", 4"
sockets 1/4 drive 3/16 to 9/16" short
sockets 1/4 drive 3/16 to 9/16" deep
universal joint 1/4 drive
bitholder 1/4 drive
Breaker bar 1/4 drive
ratchet 3/8 drive
extensions 3/8 drive 3", 6"
sockets 3/8 drive 1/2" to 1"
sockets 3/8 drive 1/2 to 1" deep
ratchet 1/2 drive
extension 1/2 drive 6"
universal joint 1/2 drive
sockets 1/2 drive 7/8 to 1 1/4 deep
adapter 1/4 drive to 3/8 drive
adapter 3/8 drive to 1/2 drive
reducer 3/8 drive to 1/4 drive
reducer 1/2 drive to 3/8 drive
Breaker bar 3/8 drive
Breaker bar 1/2 drive
Adjustable wrench 1" opening
adjustable wrench 9/16" opening
Hammer, ball peen 1 lb
Hammer, cross peen 1/2 lb
Mallet, rubber /plastic
set of punches
aluminium drift 3/4" dia
aluminium drift 1/2" dia
straight edge, 12"
File, half round, 6"
File flat 6"
Set of needle files
Vice grip pliers
Needle nose pliers
Water pump pliers
Pliers for electrical connectors
Wire locking pliers
Allen key set
Tap handle (ratcheting type)
Ratcheting box wrenches 1/4" - 7/8"
For sheet metal and compositesI would add:
die grinder, 90 degree and straight
90 degree airdrill for threaded drill bit
or with collets (there is a good British make (Desoutter) you can gring down ordinary drill bits. it takes very little space)
rivet gun with regulator
Flush rivet snap
basic set of bucking bars (often the tool crib has special bucking bars around)
Microstop holder 9/16 dia (cutters are usualy supplied by company)
1/4 drive air ratchet
Clecos in standard sizes
Aviation shears, 1 set
Straight edge 6"
automatic center punch
Pop riveting pliers
Torque wrenches, crimping tools and bigger tools are usually supplied
Even so your toolbox will be quite heavy.
I got myself a toolcase for my basic tools from Chicago cases made of high impct plastic with wheels and a pulling handle in case I´ve got to fly to some outstation to fix an AOG plane. The interior has been modified by myself. It can be loaded without problems as baggage or cargo.
For my sheet metal tools I´ve got an extra metal box.