Getting the bag and 100ml containers for flying with liquids in hand luggage

In the EU, the bag must be a transparent one-liter re-sealable plastic bag. Nobody is going to measure or question your bag as long as it looks like everyone else's, so any standard quart sandwich bag like you'd buy at the grocery store is fine. Some people buy specialized pouches intended for this purpose, but there's no need: an ordinary freezer bag is cheap and lasts quite a long time.

I often buy toiletries for travel that come in 100ml (or smaller) containers, which avoids the annoying process of pouring into smaller bottles. These can often be found at drug stores. If there's a particular product you want that isn't available in travel-sized bottles, you can buy 100ml containers at some drug stores, housewares stores, travel/luggage stores, and online.

Containers are required to be 100ml or less, and you risk having the items confiscated if yours are larger. You well could get away with a slightly larger bottle, but it's your risk.

I have had a brand new 110 ml bottle thrown away by TSA, so I would suggest staying within the 100 ml threshold. Sometimes, the travel sizes products are expensive and so will really depend on your choice whether filling it in a small bottle or getting a travel size piece. I personally do a combination of both! Regarding the bag, as already suggested, any ordinary ziploc or sandwich bag should work. As long as they are able to see everything, you are fine!