I am training manager for my airline.
Personally, I teach 747-200 pilots, and F/Es, classroom, simulator and line training.
I am TRE-TRI... so, excuse me, but I think I know a little about how to...
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If you never went through TR training, dont go study by yourself.
You might end on the wrong track, especially if using "other airlines manuals".
However, if you have the actual manuals, and decide not to listen to my advice...
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Best sequence of system and procedures studies - Boeing 747 (classroom)
Can adapt following sequence to 737 (and 727 as well)...
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(1) Electrical system -
Electrical`power sources, engine and APU generators, external power, AC distribution, DC power and distribution and buses, memorize items on essential bus, items on stanby bus, hot wired items on hot battery bus.
Study electrical limitations, memorize recall items of loss of all generators.
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(2) Fuel system -
Fuel tank layout and fuel distribution, fuel servicing, capacity of tanks, fuel pumps and shutoff valves, fuel transfer and jettison, fuel heat. Fuel system limitations.
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(3) Powerrplant -
Engine design and type, engine limitations, ground and flight start, engine lubrication and cooling, engine fuel system (FCU), bleed air valves, reversers. Fire detection/protection.
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(4) APU -
Design, limitations, fuel control, in-flight use limitations if applicable, fire detection/protection.
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(5) Pneumatic System -
Distribution and ducts, engine bleed valves and controls to A/C packs, temperature limitations.
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(6) Air Conditioning -
Temperature control (cabin) and cargo hold, cabin distribution, zone controls,
aux electric heaters. Automatic and manual controls of A/C. cargo hold (belly) fire detection/protection. Smoke goggles and smoke equipment, portable O2.
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(7) Pressurization -
Cabin pressurization limits, outflow valves (auto and manual control), loss of pressurization check list (memory items), Oxygen system, portable O2 - emergency descent check list (memory items). Profiles for descent, speeds etc.
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(8) Anti-Ice -
Engine anti-ice, wing thermal anti.ice, windshield heat, probe heat - For all items, study limitations.
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(9) Hydraulic Systems -
Engine driven pumps (air driven pumps), hydraulic systems distribution. Gear and brakes, anti-skid, alternate extension of gear, limitations.
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(10) Flight Controls -
Trailing edge items, leading edge items, hydraulic and alternate electrical operation, limitations, outboard/indboard ailerons, spoilers, rudder, stab trim, CCA and autopilots A/B/C... limitations.
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(11) Flight Instruments, communications, navigation -
Power sources (P Panels, buses), operation of autoflight, flight instruments, speed limitations, flight directors, warning lights and aural warnings.
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(12) FLIGHT OPERATIONS MANUAL (FOM) -
Memorize all limitations and review memory recall items.
Study non-normal/emergency check lists.
Performance, takeoff, climb, cruise, landing tables. Fuel required.
Weight and balance (passenger and/or cargo aircraft).
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(13) Written Test - 80% grade pass...
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FLIGHT CREW TRAINING MANUAL (FCTM) -
(Start study FCTM before simulator training)
Check list, appropriate knowledge of check lists and procedures.
Initial training for type rating as follows -
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(A) Sim training - NORMAL OPS (2 sessions PF, 2 sessions PNF) - VMC
Normal takeoff, climb, cruise, stall recoveries, steep turns 45º bank, speed control, descent, approach, normal landings landings.
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(B) Sim Training.- INSTRUMENT PROCEDURES (2 sessions PF, 2 sessioms PNF) VMC/IMC
Normal takeoff, climb, area departure (SID) - holding, speeds for holding, approach and landings ILS, VOR, ADF, missed approaches. Cat.II ILS procedures (PNF).
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(C) Sim Training - ADNORMAL/EMERGENCIES (2 sessions PF, 2 sessions PNF) VMC/IMC
Engine failure before V1 (reject), after V1 (climb), engine out ILS, VOR, ADF, to full stop landing and to missed approach (engine fire) - 2 engines out approach (VMC at 800 ft AGL) Decision to land. Abnormal flight control configurations.
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(D) Oral exam (2 hours) and Simulator Check (PF and PNF) - 2 hrs
If PIC qualification, must include 2 engine-out maneuvers and landing.
If SIC only qualification (cruise co-pilot) V1 reject and emergency descent not required.
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Hope this will assist you...
Do not forget to settle the bill for beers after debriefing (when I am TRE...)

Happy contrails