'Newb' - All my Mountains are Paved...

I'm just getting into Online Bike Forums after many years of campaigning a Trek and now a very used and partly rebuilt Rocky Mountain.
My biking involves City Curb and Pothole Jumping, On and Off the Bus' front rack, Over the shoulder to carry it up Train Steps and Escalators, & step-walking the granny-gear up some of the San Francisco Bay Area's finest hills and inclines.
My front gearing is a three-set, but I haven't yet counted teeth, front or back.
Front Derailleur is non-existent; I slapped a poor fitting one on just to help with the chain jumping off.
(That symptom is going to be the main reason why I'm here, more on that later.)
The Rear End is a (I think) a Freehub with the 7 speed cassette transplanted over from the 'could not be trued any more' back rim.
I'm being counseled that I have worn gears and it's time to swap old mech for new.
I had grand thoughts of upgrading to an 11 speed set up, but the rear rim is new and sturdy like I like it so-
sticking in the 7 speed arena for now.
The stuff I've been picking up lately is:
Thick-Thin is a thing,
only having one (or maybe just Two) front chain-rings ain't a bad idea,
and I really need a very large 1st gear on the back, Granny-gear for the Win.
Maybe even the first two back there being on the large side.
I'm going to try and participate here pretty regularly but right now i need to break out the metal ruler and the calipers and document just what I've got and have been taking for granted.
My biking involves City Curb and Pothole Jumping, On and Off the Bus' front rack, Over the shoulder to carry it up Train Steps and Escalators, & step-walking the granny-gear up some of the San Francisco Bay Area's finest hills and inclines.
My front gearing is a three-set, but I haven't yet counted teeth, front or back.
Front Derailleur is non-existent; I slapped a poor fitting one on just to help with the chain jumping off.
(That symptom is going to be the main reason why I'm here, more on that later.)
The Rear End is a (I think) a Freehub with the 7 speed cassette transplanted over from the 'could not be trued any more' back rim.
I'm being counseled that I have worn gears and it's time to swap old mech for new.
I had grand thoughts of upgrading to an 11 speed set up, but the rear rim is new and sturdy like I like it so-
sticking in the 7 speed arena for now.
The stuff I've been picking up lately is:
Thick-Thin is a thing,
only having one (or maybe just Two) front chain-rings ain't a bad idea,
and I really need a very large 1st gear on the back, Granny-gear for the Win.
Maybe even the first two back there being on the large side.
I'm going to try and participate here pretty regularly but right now i need to break out the metal ruler and the calipers and document just what I've got and have been taking for granted.
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Let us know what gears (numbers of teeth) that you have on the front and rear and we'll be able to help you get the same or better gearing with fewer front rings.
You need to be sure if you have a freehub with a cassette at the back or a spin on freewheel.
Sunrace do some reasonably wide 7 speed cassettes
http://www.sunrace.com/en/products/detail/csm40
retired 9.6kg Carrera Kraken
The Carrera Hardtail combined thread - come on all you Carrera's!
The Sons Scott Genius RC20 build
So that's what he meant by "thick-thin is a thing".
So far I can report I have a Front Three Ring (circus) w/:
22/32/42 & I only got to counting the 1st Gear on the back as having 30 teeth.
The rear is indeed a hub w/ Splines (vs any kind of spinning-on type arrangement.)
I've only ever really looked at Rim circumference (26" vs 700mm- which is what I have btw, 700)
I'm hoping I have enough Derailleur to deal w/ a 32 or 34T 1st gear. I'd rather have a larger range in the back, even if I had to trade off from the current Three-rings up front to a Two Ring setup.
btw- Thx Rookie; I had no idea you had to do a Single Chain Ring to use thick/thin hardware.
PS- http://www.sunrace.com/en/products/detail/csm40 Ooooooh, 34T & it's Blacked Out too...
You can probably fit a single 32 or 34 tooth chain ring* and one of those Sunrace 7-speed cassettes without any problems. It's worth fitting new jockey wheels and chain while you are at it as everything is probably worn.
What bike are you talking about - model and year?
*Assuming the chain rings are removable on your chain set.
And it all promised so so much”
Giant Trance 2 27.5 2016 ¦ Bird Zero Mk1 ¦ Giant Revolt Advanced 2 2019 ¦ Giant Anthem 3 2015 ¦ Specialized Myka Comp FSR 2009
btw- it's a Rocky Mountain, year unknown. The frame was on the way to the Recyclers when I salvaged it.
The Front Shocks grew a stress fracture over time; replaced them w/ a fixed fork for now.
Rear Derailleur Drop-down stripped out after getting my rear rim 'tacoed' by a car leaving a parking lot so I'm using a simpler Shimano over-the-axle unit. That drop-down (correct term?) - edit - Hanger Is modular though so I have expectations of finding a replacement...
I picked up a set of front combo shifter/brake levers recently. They too are Shimano & 7 speed, (pretty sure SIS but model # is forthcoming).
https://drive.google.com/file/d/1VTPobh ... sp=sharing
I'm having 'fun' w/ Google Drive, But those links are for the Rear D., and front left shifter/brake mech..