On thing to bear in mind if booking lots of flights seperately with different airlines, if anything does go wrong during the journey and you miss connections, the inbound airline is not responsible for re-booking you/paying for it etc, and you are on your own to sort that out. Then it could end up costing a fortune as you could then have to pay a difference in the fare to get on the next flight for example - providing they actually have space !!.
Thats why it costs a bit more to book it all together on one ticket/itinerary, then if anything does go wrong then you will be sorted out.
If it all goes ok though, you can save quite a bit, but thats the risk you have to take.