Motherboards:
The Jetway all the way.
Jetway is a pretty low-end brand, but still better than PC Chips - and this particular PC Chips model (M537) was notorious for a 5V>3.3V voltage regulator that couldn't take the load and tended to fail spectacularly taking the board and frequently CPU down with it. Also the Via VPX chipset is pretty lacklustre. The Jetway board has a SiS 5571 chipset, which was actually pretty good - not a top performer, but solid, with a mix of i430VX and i430HX-level features plus UDMA 33, which both lack.
As for the VGA cards, what OS do you want to run, and if DOS what kind of games?
- in DOS the ARK2000 is probably the fastest PCI option you can find. Its Windows performance is poor however. Its VESA SVGA compatibility is good, but not perfect.
- S3 Trio gives much better Windows 2D performance and only very slightly lower DOS performance. Its VESA SVGA compatibility is also good, but not perfect - with different issues to the ARK2000. A lot of S3 cards suffer from poor analog output quality (blue or yellow discoloration) - although not all, so check your specific cards - particularly the Trio64v2/DX, which looks to be of very cheap build quality.
- Oak is notoriously slow in DOS and Windows, but VESA SVGA compatibility is pretty good too.
Two points:
1) VESA SVGA compatibility is frequently less of an issue than it is made out to be. It's only relevant to DOS SVGA games and even within that relatively small selection, only a handfull are notoriously difficult. Take a look at this overview. If you intend to play one of the games listed, be sure to choose something that plays nicely with it. If not it's entirely possible you will never face issues, so don't over-think this one, certainly not when all your options have above average compatibility anyway.
2) with vintage PC gaming, faster is NOT always better. In particular a lot of older DOS titles are speed sensitive and can be unplayable or downright buggy if your system is too fast. So there may be games that play better with the Oak card than the Ark card 😮
As for sound cards...
You say you have AWE32 and AWE64, but you post a pic of a CT2770 SB16. The Sound Blaster 16 range are a solid choice for software compatibility, but all are buggy in at least one way, sometimes multiple bugs, and sound quality also varies, with earlier models being noisy and later models having a Creative-designed 'CQM' FM-synth chip instead of Yamaha's OPL3, which many consider to sound worse. Exactly what to expect depend on the exacct model, and in some cases (such as your CT2770) it can even differ within a single model on what chip Creative was using the day your was made. Here an overview.
Your CT2770 has minor hanging note bugs in MIDI, it has slowdowns when high quality digital audio is played at the same time as MIDI music, it shares with all early SB16 occasional clicking sounds and it may be noisy depending on the version of the CT1703 DAC. Yours has the CT1703-T, which is intermediate - not terrible but not noise-free either.
The MIDI bugs are only relevant if you use the MPU-401 MIDI interface on the card with an external MIDI device. Yours doesn't have a wavetable header, so that would mean using an external sound module (something like the Roland SC-55)
If you do actually have AWE32 or 64, look up the exact CTxxxx model number. Here again, what you play and what sort of bugs bother you will determine which is the best choice. Early DOS games make a lot of use of FM synth, and later SB16 cards (including all AWE64 and some AWE32) have that CQM. If you play them, an earlier card (such as the CT2770 or an early AWE32) would be better - unless you actually like how CQM sounds (lots of comparisons between OPL and CQM on Youtube). Later titles tend to use more digital audio and MIDI (if you have a MIDI device, of course). Only the very oldest and newest (AWE64) SB16 are free of MIDI bugs and in particular you REALLY want to avoid the cards with the 'type 1' hanging note bugs. The AWE64 give nice clear sound, but CQM FM. The earliest SB16 give bug-free MIDI and OPL3, but are noisy as hell. Or break out the soldering kit - you can replace the DSP of a mid-period SB16 to get OPL3 and bug free MIDI - but you'll keep the single cycle DMA clicks.
TLDR: SB16s are a buggy mess. If you care about how it sounds, you can dive really deep down the rabbit hole. Or do what I did: ditch the whole steaming pile and go with a clone; SB16 clones are rare but they exist and a good one gives the magic trio of no MIDI bugs, real OPL3 (or 1:1 clone) and no self-noise. However compatibility is less than 100% and a lot of cards with them tend to be of poor quality. Chips to look for in that case are C-Media CM8330 and Avance Logic ALS100 (*not* ALS100 Plus which lacks high DMA support).