Running 20amp for your workbench is a good idea (and be sure to use 12/2 wire), but overkill for a computer circuit: most residential circuits are 15A and are run on 14/2.
You don't have any choice in the breaker: Siemens panels only accept Siemens breakers, and StabLok panels only accept StabLok breakers (and of course there are several other brands). The bus design in each panel is different, and so other brands of breakers won't fit. This isn't the full truth: there are other companies that make breakers that are compatible with Siemens panels, but they'll be marked that way. Just realize there are different designs of panels with different designs for how the breakers physically connect in, and they're not all cross-compatible.
There are some known problems with the design of StabLok panels (which are made by Schneider Electric, and sold as Federal Pacific, Federal Pioneer, StabLok). InspectAPedia has some pretty dire warnings against using FPE StabLok panels - I was actually not aware of the extent of problems until just now. According to the article, it's actually a fire hazard as they can come loose, and that's aside from the apparent defects in the breakers themselves (they can fail to trip, and even fail to shut off when you manually turn them off).
I personally am not a huge fan of StabLok, the connection is just not as solid as you get with, eg, SquareD panels, and most StabLok panels are ugly for that reason: all the breakers are skewed in random directions.
That Federal Pacific panel has to go as they are dangerous. As far as concerns about your skill, you sound like that particular kind of newbie who is well capable of learning to do it all safely and well; however my hunch is you are still thinking too much, and need to read a little more. It's OK, we all start there.
Normally, just replacing a sub panel is a straightforward thing. Change panel, reattach wires, done. However, this is only part of a project with a much larger scope. You must contemplate (i.e. ask your permitting authority) whether you have crossed the legal threshold of a remodel. If you have, everything in-scope must be done to all current codes. Even ADA!
The 2-circuit requirement for kitchen outlets is not intended to mean "1 circuit for this wall, 1 circuit for the other wall". I'd encourage some more research but if it was me, I'd interleave the outlets, every other outlet on a different circuit. Also there's nothing wrong with more than 2 outlet circuits in a kitchen, the whole point is to prevent trips when the chef is madly at work, so the chef isn't hobbled with limitations like having to put the toaster here and the George Foreman over there, and avert ugly workarounds like extension cords draped across sinks or stoves, etc.
I see you plan to go 12 AWG wire for almost everything (that's what 20A breakers mean) - that's awesome. Feel free to kick the refrigerator and smoke detector up to 12AWG also - that way you don't have to buy any 14AWG wire. I don't own any! If you have some other reason to use a 15A breaker you are welcome to use that on a circuit wired in 12AWG.
You may want to run the water heater circuit in 10/2 or even 8/2. That will allow you to easily upgrade to an electric water heater in the future. Still use a 15A or 20A breaker because the outlet is still only good for 20A. There is a trick to fitting 8+ AWG wire on a 15-20A outlet, just ask.
I would go with a much larger panel. You have either -1 or 3 circuits left, and that's too little headroom for my comfort. Getting a larger panel is dirt cheap compared to the cost of replacing perfectly good breakers with duplex breakers (I call them double-stuff) merely to shoehorn everything in. Also, larger panels in combo-packs come with more breakers and that is far-and-away the cheapest way to buy breakers. Another reason to avoid duplex breakers is if you ever need AFCI, GFCI or whatever future thing comes out - those are much more expensive in duplex breakers because of the miniaturization required. Don't think you must use a 100A panel - you can use a larger panel (200A), you just can't use a smaller one (70A).
Remember each sub-panel must have its neutral bus bar separate and isolated from its ground bar. That means removing bond straps, magic green screws, neutral bar kits, whatever the panel requires to do that. You might consider a panel with a neutral and ground bar on each side of the panel. That's a convenient feature so wires don't have to cross over the panel.
Keep in mind how your house got a dangerous Federal Pacific panel. The last guy bought cheap. Feel free to research the good-better-best that each manufacturer offers, the price differential for "best" is quite small compared to the overall cost of a remodel. You may find better selection and better prices at a real electrical supply house.
There is nothing wrong with more ground rods. Go nuts. The key is that all the grounds are connected to each other by wire - and they are not connected to neutral anywhere except one place - the main service panel.
Best Answer
I have good news...
Your panel is not one of the dreaded FPE firestarters. Trumbull panels appear to be ancestors of the modern-day GE loadcenter line, although I have not yet been able to ascertain if your panel is forward-compatible with modern GE (THQL) breakers.
and bad news
However, these old Trumbull Electric panels do have a design defect: the upper row of breakers is "upside down"! In other words, you have to flip breaker handles in the upper row down to turn them on and up to turn them off, which violates NEC 240.81: