Rachylou has the right of it. Since DH checks his often bigger bag, I'm going to wait around anyway, so I check mine. However, I have brought it aboard without problems. I do not trust the advertised dimensions, and have a mini measuring tape in my purse. (Comes in handy for all kinds of things.).
My bag of choice is branded by Air Canada, and measures 20 inches, 20.5 with the wheels x 14 x 7 ( but can bulge to 9). It is not a spinner. Packed full, it usually weighs in at 20lb. It fits in the overhead compartment of planes, busses, and trains without any problem. This is the suitcase I used for 4 weeks in the UK on 3 separate trips, during the months of April, July, and September respectively. Also shorter trips to Norway, various Caribean destinations, or just a weekend getaway.
Although I might very well pack some favourite comfy clothes over which I would shed a tear if lost, I don't bring anything too precious with me when I travel. I also like to have some room for purchases, and might very well purchase clothes, and put them into rotation, when abroad.
3 bottoms (one worn on plane) 10 tops (ditto), a leather jacket, jean jacket, trench was all I needed. I always bring a bathing suit, 1 yoga Capri, hat, and gloves or fingerless mitts, as well as a pashmina scarf. Underwear, and socks of course. 3 pairs footwear (one pair worn on plane) and flip flops. This is good for 10 days - 2 weeks. (I don't mind doing laundry enroute. It can be an adventure and you get to mix with locals. There are some very nice laundromats, too!).
The yoga Capri works with a T-shirt for a cover up over the suit if there is an opportunity to swim or spa. It works as a cover up in lieu of PJ's as well, or when just lounging in the hotel room. The flip flops are in lieu of slippers.
FWIW, to get through airport security easily, dispense with the fancy cosmetics bag, and use a couple of zip lock freezer bags. Put them in one of the pockets on the front, and when you go through security all you have to do is pull them out and lay them on top of your case.
Also, try to avoid belts, jewellery, and thick soled of heeled bulky shoes, or shoes with ties. Also clothes with lots of hardware, grommets, etc. These are all things that will set of alarms, and will have to be removed, scanned, and then put back on!