Our organization is planning to peer with the local internet exchange, we are planning to obtain an AS number to allow us to do this. However I was unsure if we also need our own IP address space to get connectivity. Would anyone be able to clarify this?
I think you are either confused or using the wrong terminology. When you "peer" with someone, that means that you exchange traffic with them, more or less as equals, that is between your customers and their customers. The traffic must either originate or terminate on one of the peering networks or one of their customers. You cannot use a peer to reach any network this is not a customer of theirs.
The concept of "peering" is that both providers are at the same level. It is not a form of Internet access -- where one entity provides another with access. (That's called "transit".) Unless you either are Google or peer with Google, for example, you cannot send traffic that is from or to Google over a peering connection.
Most large networks have onerous peering requirements that you will not meet. You will, at a minimum, need a national network. Otherwise, they will have to do the long haul on coast-to-coast traffic in both directions. That's obviously not fair. If you want to peer with someone, you have to split the work close to 50/50. That means you have to do half the long hauling.
You won't be able to pick up many International routes for the same reason -- why should someone else do all the International hauling? That's not fair, and peering is about symmetric fairness.
Essentially, you'd only be able to peer with those networks that have open peering. And you'd need someone on your staff who understands peering in great detail and can coordinate your operations with other networks. Theoretically, so long as you qualify for a large enough block of IP address space from someone, you can peer using that address space. (Though some providers do include minimum address space as part of their peering requirements.)
Why are you looking into peering? Why are you going to an exchange? If you are looking for cheap Internet access, doing all the work yourself is definitely not the way. You lose out on every economy of scale there is.
If you're imagining that this will get you anything that looks like Internet access, you are seriously mistaken. The exchange cannot force another network to peer with you unless they wish to, which will again mean you have to meet their peering requirements.
To be blunt, this makes no sense at all unless two things are the case:
1) You know for a fact that there are networks there that will peer with you, and
2) you know for a fact that you need (or will need) to exchange significant amounts of traffic with those networks or their customers.
Now that the OP has made it clear what he's actually looking for, I can proceed.
In order to set up a decent stable, resilient, network, you need multiple layers of redundancy on the networking stack.
You contact your LIR and ask for some PI space.. Good luck with that. You'll need a minimum of a /23 or /24, as many providers refuse to advertise a block smaller than that.
You can't expect them to advertise a /27 for you, as it'd make routing tables enormous.
So you need to justify 255-512 IP addresses. Good Luck With That. IPV4 exhaustion is making this nearly impossible.
Then you'll need to contact some transit providers. Not knowing who your clients are, how much traffic you'll be using, or where in the world you're based, I can't help with this decision.
Then you'll need some hardware. You need 2 big fat routers. Cisco or Juniper. As long as they can do BGP and handle a full table (512MB of router ram or better).
Then you'll need a sysadmin who understands BGP. I mean, really understands what a MED is, and why you use it, and what communities are for. You'll be looking at someone well trained, and probably highly expensive.
Then you need to get your sysadmin to make it all work together. Might as well make sure he's got a Company AMEX, because it'll cost money, things need to happen, and yes, it's not cheap.
If you find that 50% of your transit traffic was going to one particular AS, then you might like to ask them to peer with you, for mutual savings on yours and their transit costs. That's why you peer. No other reasons really.
What you say is like "I want a number plate for a car, not sure I need a car for it". An A is an autonomous system (that is where AS comes from) of independently routed IP addresses. WIthout addresses there is no AS. So, you get it backward even here.