Bicycle Mechanics - A battery of questions loosely involving Rear casette problems! 1996 D'back podium1.0

I have a habit of talking and/or typing way too much. I will do my best to convey what I need while avoiding the horrible INTERNET TLDR problem. (Just finished the post - I failed folks)

That said, I have a probably not so unique situation: I picked up what seems to be a (1996?) diamondback podium 1.0 frame for about 100 at a community bike warehouse, and the only remaining things attached were the rear brake calipers and integrated shifters - thank the lord.

I have volunteered in this bike shop for several months over the course of the years I lived in town, and am somewhat of a spotty knowledged, amateur mechanic. It started out with fixing flats, but nowadays I can restring brakes and adjust all manner of brake calipers and derailers and this and that.

The bottom line is I slapped what should have been basically stock everything back on the bike, the brake calipers match brands and fit the frame, shifters work forward and back on both sides, wheels are great and I have had a great time riding for the most part. The problem arises I BELIEVE in the rear cassette, and the chain, and so begin my battery of questions.

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The only cassette that fit and was in the shop that day was an 8 speed road bike cassette, of which the brand name I don't know. When I put it on it was baaaaasically having a bad day. Each sprocket could rotate independently of the rest, a trait that is frowned upon for gear systems. Fortunately with a wrench on hand I tightened it up to a workable level, and slapped the matching chain on.

1) This chain had one fixed link, I bent and smacked it until it was workable
2) The smallest sprocket is warped, though still usable.
3) Probably as a result of non optimal casette+chain, there is rubbing on the front derailer for a good amount of gear ratios.
4) Shifting is mostly workable, though it seems like I'm not getting a full 8 out of the rear gears. possible skipping.
5) One particular gear seems to 'jump' about the same place after every few pedals, possibly the chain link issue?
6) When using the non jumpy gear, the bike works wonderfully, but the weird gears are in the middle. I know about derailer limit screws, but not about tension adjustments.

So that was my probably TLDR history of me and this bike. My actual intent is to probably just buy a rear cassette that isn't broken from day 1, and to replace the chain along with it. The forum tips suggested to hit up shimano's helpdesk, but I believe this bike might be too old?

How would I go about finding a working 8 speed rear cassette that is spaced right? And its companion chain?

What do any of you gurus think about the issues I described? In the time before I get a new cassette I can probably fiddle with the derailer, any advice?

-16 speed
-Diamondback Podium 1.0
-Shimano rx100 shifters, front derailer
-Shimano 105 rear derailer
-Busted questionable name rear cassette
-Shimano SG A-53, A-42 Front Sprocket

Have you measured the chain? A new chain should measure exactly 12 inches per foot (24 pins). All chains should be replaced by the time a any one foot interval has stretched to 12 1/16 inches.
What brand is the rear hub? If it is Shimano the cassette is probably Shimano or SRAM.
Are you sure it is a cassette and not a freewheel?
If you want to learn the correct way to set up and adjust derailleurs, including cable tension, go to www.parktool.com.

... Each sprocket could rotate independently of the rest,

I can't see how this can be happening. Freehub bodies are splined, with the matching splines stamped out of the sprockets. Only cases of spinning sprockets I've seen is when someone has tried to run loose sprockets on an aluminium body, where it's possible for the steel sprocket to shear a path through the aluminium splines.

And torqueing down hard enough to get a sprocket w/o the spline engagement to stay put while riding seems equally improbable.

You have a mix of 7sp and 8sp stuff going on there.

1. check whether your rear shift lever is 7sp or 8sp in reality. Click through the shifts, calling the initial click "two" since you were in the first detent already.

2. if the shift lever is 7sp, get a 7sp cassette and a new chain. I don't think your rear hub will allow an 11-tooth cog, so pick something that starts with a 12T. Tangentially, if your existing cassette does start with an 11, that's probably why the cassette stack isn't snugging up. Shimano HG-series cassettes such as the HG50 and HG70 would be good, and a SRAM PG830 chain would work OK there. edit: Oh, and with a 7sp cassette on an 8sp freehub body, you'll need a spacer to take up the extra room.

3. if the shift lever is 8sp, get an 8sp cassette and a new chain. Same caveat as above, use something that starts with a 12T or larger. A SRAM PG850 in a 12-26, paired up with a SRAM PC830 chain, would be a relatively affordable setup for 8sp, or there's Shimano equivalents too.