choosing a backpack

Try before you buy. Include the amount of weight that you anticipate in the pack while fitting.
https://www.rei.com/learn/expert-advice/backpacks-adjusting-fit.html

Note that full size carryon bags are too big to fit under the seat and some seats have less underseat space than others.

I agree with the above post about underseat space. You can have a lot of room or no room at all (Alitalia). I would plan on a bag that can be placed in the bin and just asking a fellow passenger for help.
Your other option is to pack very, very little and use a RS Appenzell or Patagonia Lightweight tote (has backpack straps; expensive - Wait for a sale) or similar. (A pack that is 25 liters or less). Stay with a pack that is under 20" long - about 18-19". Use Packing cubes. (consider eagle creek tote with backpack straps on it.)
Look at Eagle Creek Converge or REI.com

I don't believe a full appenzell would fit under most seats. We have 2 and I love them, but you can pack quite a bit in them.

Have you looked at this pack by REI? REI Co-op Ruckpack 40 Pack - Women's, https://www.rei.com/product/118816/rei-co-op-ruckpack-40-pack-womens . It has good write-ups in both the mens and womens versions.

I used a Rick Steves Veloce for several years but it is wide so there is no room for feet when it’s stashed under a seat. I made an impulse buy at my local AAA right before a domestic trip and it works well. It’s a LiteGear Mobile Pro.

https://litegearbags.com/product/mobile-pro/

Pluses: it’s skinnier than the Veloce but a little taller. Might be too long for your back. I like how the pockets are laid out. Cute accessories including a lunch box.

Minus: I don’t like how the shoulder straps fit. They seem too wide. I could not use this for a day of hiking as one strap rubs my armpit but it’s fine thru an airport. I just finished an RS Tour and it worked great as a bus bag.

I don’t use this as a primary suitcase so you’d have to see if it would work for that.

If you have an AAA store near you, see if yours carries it. The store items vary widely.

You’ll need to limit yourself to 25-30 liters maximum. A full size carry on will not fit with today’s airline configurations.

You’ll also have to look at the thickness of the bag - no more than 7 or 8 inches thick.

Length is also an issue. I’d say no more than 18-20 inches.

I use the Patagonia light weight Travel Tote. That is a 16 liter bag and I’ve never had problems with it.

You may also want to think about a duffel. Some of the light weight day packs from Osprey are nice. Something like the Daylight Plus.

We selected the RS appenzell because of several reasons, but one was it had to fit under the seat in case of forced gate check. We had a 13.2 lb weight limit and 7.8 inch depth limit and it was great for a couple changes of clothes, electronics, paperwork, 311, water bottle, snacks and the girls had their sandals in the bottom. The appenzell can hold a ton and stretch to much bigger but it was perfect for us with a small checked bag (20-22 inch), which were not packed full on the way over.

Consider the absolute least amount you can pack - then, find a bag that works for you. Get packing cubes to help. A small "underseat" pack, as your only pack, may be insufficient depending on how much you are bringing. You can also check a bag. Or, just ask a fellow flyer to help you load a bag into the overhead bin.

First, to the OP: you should edit your post to remove your email(!) - a lifetime of spam is headed your way.

Second: I think your plan to get your bag under the seat in front of you is noble but misplaced. Most long-haul airline seats have a large (sometimes shockingly large) metal box underneath that house the electronics for that row of seats' in-flight entertainment screens. Depending on the seat layout (every airline/plane is different), chances are that you will get stuck in one of those seats, and you will simply not be able to fit anything even close to "carry on size" under there. You may get lucky for a flight or two and the guy next to you gets the box, but it will happen to you soon enough.

I recommend you plan to travel carrry-on only (no checked bag), which means the bag needs to be reasonably sized. That means about 21" tall, 14" wide and 9" thick (maybe a little smaller for some low cost carriers, especially in Europe and Asia - alas, there is no universal standard). That bag should go in the overhead bins - that's what they're there for. Folks of a shorter stature should climb on the seat if needed or seek help from taller folks nearby.

Just ask for help we always help people put their bags up so people can situated and the flight can leave on time.

There are mini suitcases like the EagleCreek Expanse wheeled tote and the ebags Kayla underseat bag. Only problem - may not be big enough for you. Somewhat rigid and may still have to be placed in a bin if your underseat space is small or nonexistent as mentioned above.
Don't be afraid to check a bag if needed. It's not a crime. Many travelers, including my own family has checked bags from time to time.