You can take a light buggy and an infant car seat as standard, even if the infant is sitting on your lap and has no luggage allowance. The cabin crew will give you a small lap strap for the baby which attaches to your own lap belt, and this must be worn for take off and landing. If you want the baby in the car seat, you will need to purchase a seat for it on the plane. It would be best to buy a travel bag for car seats and check it in with the luggage. You are often allowed to keep the buggy until boarding, but don't rely on getting it back when you disembark, it may well go to baggage reclaim and you can get it back there with your cases. If you can manage without it check it in as well, you can get buggy travel bags too. Use a sling or carrier for the baby which will leave you hands free for managing passports/boarding cards/ plane stair rails etc.
Most people opt for an umbrella folding buggy, but you could take a Petite Star Zia or a Baby Jogger City Mini which are compact and light. You can get bargain Zias which are mostly catalogue returns or have slight faults like imperfect stitching from nurseryvalue.com; which have been reworked and are almost like new. I have seen what baggage handlers do to luggage, and they are no more careful with buggies, so taking an expensive one is a risk. You can get nice liners to make buggies more comfortable for little babies too.
If you want to take baby formula with you, powder is fine; you can have a sterilised bottle filled with boiled water from an airside cafe and make it up before you board. You can pre-order liquid formula cartons from Boots branches airside, which means you get around the security problems. But the worst that can happen is you will be asked to taste it, they won't take it off you if you have a carton with you, just have a bottle to pour it into because you can't re-seal cartons!
An important detail also is that baby toiletries are subject to the 100ml rule and have to be in a clear plastic bag through security. However, baby wipes are exempt! If you think you will need nappy cream, Bepanthen do some individually wrapped wipes with the rash formula on them which could be useful. Also be prepared for nappies to be very expensive compared to here.