Most airlines allow two carry on bags. If you carry a small to medium sized purse, for the love of all that is beautiful, pack your purse inside of a backpack so you can pack more items in the backpack Alternatively, consider putting all of the allowable carry-on items for your purse into an organizer and carrying a huge tote bag and packing your purse in checked baggage.
I like to pack full-sized toiletries. If I'm going for more than a week so these items must go in checked baggage. It's extremely important to pack in an organized way which includes not putting prohibited items in carry on. They'll just make you throw it away.
Also, be aware that at some airports the baggage check outside belongs to the airline is free and at other airports, those baggage checks are contractors and they charge to check. I once made the mistake of standing in that line, wasting time and getting looks of disdain from other passengers.