I thought I would take "notes" and eventually end up with some good information. See References at the bottom of the page.
tl;dr : The best N64 Motherboard for modification is: NUS-CPU-04
Approximate US Serial Numbers NS135731008 to NS204554187
Why:
Possible Modifications:
This modification has 2 variants
Facts
The Mod involves removing the 2 qty 2 MB RDRAM chips from an early motherboard and replacing them with 2 qty 4 MB RDRAM chips either from later Console revisions or Expansion PAK's.
The remaining question is whether to use the Jumper PAK or another Expansion PAK, that determines if you have 8 MB or 12 MB. Honestly most games can't take advantage of anymore RAM and some may fail completely because of assumptions the programmers made about RAM size.
I've read that this RAM modification is just a solder fix, but I have not personally seen or performed this modification.
Cross Reference Console Serial Numbers:
http://nintendo64.wikia.com/wiki/Console_Serial_Number_Guide
Serial Numbers notes:
It really matters which Motherboard, not the Serial Number, but there isn't another external indicator of which Motherboard is inside the console. Opening the console up is the only 100% positive way to tell.
Motherboard Revisions:
NUS-CPU-01:
NUS-CPU-02:
NUS-CPU-03:
NUS-CPU-04:
NUS-CPU-05:
NUS-CPU-05-1:
NUS-CPU-06:
NUS-CPU-07:
NUS-CPU-08:
NUS-CPU-08-1:
NUS-CPU-09:
NUS-CPU-09-1:
Some content and ideas are from a now archived site: kyorune
A lot of great, yet technical RGB information here: http://www.retrorgb.com/n64.html
RAM Upgrade discussion: assemblergames
RAM Upgrade How-To: bitbuilt
Schematic of NUS-CPU-03/NUS-CPU-04
Jumper Pack replacement discussion: benheck
Heat sink discussion: modretro
Portable discussion: modretro