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What's the best method for putting in odd shaped windows into a side panel? For example, I want a series of varied width lines with triangles cut out of my side panel. What's the best method for putting a plexiglass panel window in? I'm thinking it might be best to just get one large sheet and mount it on the inside of the case (rather than U-channeled), but is that a good way to do it?

id suggest a dremel.

To cut the patterns in the panel, or just mount the Plexi?

For cutting the panel, you might check out local trade schools, high school metal shops, or perhaps a community college with a shop. A lot of 'em now have water jets or even laser cutters that they just need a simple drawing for and a scale (or too-scale to make it simple) for a pattern. Most cities or more industrial towns have businesses, and it's not as expensive as you might think. I had a panel laser cut with just a black and white pattern for $28. Took 4 days for them to get to it, but it was low on the priority list and I still think that was fast. It would have taken me 4 days to cut it out myself by hand. Dremels and small files rock, but sharp corners (like tips of sharp flame tips or scallops) or where the holes leave very little metal between cutouts (1/4" or so) and it can be a heartbreak when it turns to warped cooked bacon. It's worth a look around for someone to outsource it if it's any sort of complex design IMO. It's fun to say "I did that", but only when it looks spot on.

To mount the plexi, it might not be the "best" but I'd recommend just what you mentioned with just one big sheet. Not all panels are straight (or stay straight very long with a lot of material cut away), so what you may run into is a gap between the panel and the Plexi in spots. So whatever you use to seal the plexi to the panel with (clear liquid nails I guess), go ahead and put a thin coat all over the place. Not enough so that it squishes out and become visible, but just a skin coat. Maybe place a dab in the middle and then spread it thin with a little cheap foam brush.

Ive tried just painting the backside of the panel and then sticking the plexi to it and let it dry (redneck glue), but it wasn't a long term solution. A couple removals of the panel and it started to separate again. Maybe a year...

sorry, yeah, not the cutting - I'm going to use a local laser cutter for that - I mean for actually mounting the plexiglass into the case.

best bet for mounting is double sided tape. and just use a single piece of plexi.

What is the side made of? You might be able to use epoxy for a bond that'll last forever.

Double sided tape around the edges of the plexiglass and a single large piece of plexiglass should work well. If your design has some gaps (where the metal was not cut away) in the middle of the plexiglass, put some pieces of tap there to keep the plexiglass from bowing away from the panel. If you ever need to remove the plexiglass from the panel (for whatever reason) you should be able to slowly and carefully pry the plexiglass from the tape starting in one corner.

If you decide to go with using glue or adhesive, depending on what type of glue you use, you may need to scuff the matching surfaces of the panel and the plexiglass with 220-320 grit sandpaper to give the glue something to grip onto. If you use an adhesive like Liquid Nails or Gorilla Glue you won't have to scuff the surfaces but scuffing will make a better seal. The only problem with going this route is you can pretty much forget about removing the plexiglass without badly damaging it and/or the panel.

Be mindful with using double sided tape. it's pretty thick and if you're wanting smooth lines it will push the plexi back a bit. Go with epoxy. It will last forever and you can still pop it off if needed later.

If you want a truly professional look use hex head machine bolts and washers. #4-40's look great in black. You can also use brass head screws for a different look. With bolts or screws you're ensured of a perfect mount, ease of removal and nothing ever falling out. Even cheap screws with the heads painted give that truly "custom" look.
Use masking tape to hold the windows in place while drilling the pilot holes, remove the tape then redrill the holes the proper size for the screws or bolts used.