There are a number of checklists available for the 737 series.  This is one I created from use of the aircraft and taking into account others' lists as well.  I use the HC Alpha and Bravo, so in a couple of places it may refer to the state of switches and knobs of these. This is because I have mapped certain functions to those switches/knobs (as per Les OReilly's superb video series for SpadNext). Similarly, throttle detent is mapped to the fuel start/cutoff levers. 

I also start the 737 in cold and dark state, but have changed the settings a little to provide for a better initial state: e.g.

a) The trim wheel is preset at 5.00 to save a lot of trimming, as many of the trims are about 4.8-5.2

b) TCAS is set to standby rather than active.

c) VOR2 is turned on, on Capt's side

d) Grnd Pwr cart is connected (but not powered up), all doors are closed

e) Pilot's (Capt's) default view is aligned with the yoke

f) CDU is alive (without having to hold down menu key)

g) XPDR is set to STBY 2000

The list covers the major checklist items needed for successful yet realistic use of the 737. It doesn't have cockpit flows, but does include specific stages such as obtaining clearances to ensure the checklist items are performed at appropriate stages.  

Various changes in versions v1.0 - v1.10

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Both full shutdown and transit checklists have now been updated and numbered v1.11.

v1.11 changes
1. Yaw Damper relocated back to 'Cockpit Preparation' checks for better consistency with tutorials/livestreams
2. Fuel Flow Reset added to 'Before Taxi' checks
3. Flight Directors reset added to 'Before Landing' checks to facilitate correct FD response in the case of a go-around

I hope you find either/both lists useful. As they each consist of 2 pages only, I suggest printing them in Duplex and placing in a plastic folder.  Please ask for specific changes.