Eldon is correct. Handbag (even a very big one), cabin luggage, coat, umbrella and book/magazine is usually what you get to take in. I travel a lot as I have homes in two different countries.
Cosmetics: try to buy travel size products (US drugstores are good at that - toothpaste, deodorant, shampoo, conditioner etc. I don't live in UK so I don't remember whether Boots does them too.). Muji does great travel-size containers and see-through pouches if you want to decant some of your favorite products into them instead, and some hotels in the US have travel-size Aveda products in their rooms.
I'm a hauler. I lived in many different countries and have hauled stuff between different continents. I have lots of suitcases in all possible sizes, but I'm using them less and less as baggage regulations are becoming ever more restrictive and luggage is a lot of dead weight (it could be even 9-10 kg!)
I always use a big leather handbag for traveling - changing bag size, even when traveling without children (I often take a small evening bag or clutch along, too).
For cabin luggage, I nearly always use a weightless but sturdy black nylon backpack (inside go: clothes, my 12" laptop, adapters & cords, shoes; cosmetics to the outer pocket). I pack all shirts in one plastic bag, all dressier clothes in another, all underwear in another, and also take along an empty laundry bag.
If I travel on business and need to take along a lot of neat, pressed clothes, I have a couple of small Samsonite cabin suitcases in various cabin only -sizes (50cm, 55 cm, etc). Black, navy and dark green are the best suitcase colors, just make your bag very visible and distinguishable with a big, bright unique tag or belt - the one time I fell for a beautiful camel suitcase, it was irreversibly stained with black machine grease on its maiden voyage. I like soft suitcases, because I stuff them very full. Hard ones don't work for me. Test the wheels, you want something that is easy and featherlight to pull along and also good for your height.
Occasionally when returning from a shopping spree I use one of those big checked plastic-woven bags immigrants in poor countries all over the world use (or actually, two of them inside each other for extra durability).
For check-in luggage, my favorite luggage these days is sturdy cardboard moving cartons (those that lie flat and can be assembled quickly and taped together). Almost weightless, super-durable, and surprisingly easy to move!