We have flown twice with DS before he turned two and never booked a seat for him, he was turning 2 the day after we returned this year, but I would honestly say that it was fine having him sat on either me or DH, he also shared his sister's seat for some of the time. He couldn't actually reach the seat back games on his own anyway so he had to sit on me!

Mostly he slept on me too so that was fine.
The only time it was a little difficult was meal time, but the cabin crew were very good about bringing DH's food and then we swapped over and I had mine.
I think it's a personal choice as to whether you need to book a seat for and infant, and also there is the cost to factor in. Personally my DS wouldn't have sat in the seat anyway, and knowing this I thought it would be a waste of ££. This year they have both got their own seats, but I doubt that they will stay in them the whole time, they like their cuddles so I'm sure we will end up with them on our laps.
As for the baggage allowance, we have always taken a buggy and car seat for both DS and DD with no problems at all. I think the best thing to do is to call your airline and ask them, at least you have got the info straight from the horses mouth.