To core switch or not to core switch?

Hi,

The diagram: https://snag.gy/uXD8Cg.jpg

The question: should we have core switches or core routers connecting everything?

We're refreshing our campus network. New network is new, in a new building. All the access switches are cabled to distribution switches and everything is new there (or going to be in a while it's still being built). Then we have the old access network where all the bad habits live. Like chaining access switches to each other and old 100Mbps switches and everything...

In the new building we also have a new DC. The older data center is managed by outsourced company, their contract is ending in a year or so. They basically run a single virtualized environment for us, they have Juniper ex/qfx or something as the core thingies. New DC is managed by us.

How would you connect everything? Ring between 'coreish' switches? Full mesh? Adding core switches/routers to the picture?

I'm thinking of just connecting fibres semi-randomly between the 'core' stuff (depending where we have fibers available) and then running OSPF & BGP in the core (BGP towards the old DC network that's not managed by us). We also have few VPN tunnels & MPLS links coming in to the datacenter... currently to our old FW from the ISPs router.

New network and new DC are in the same building, old DC network is spread accross two different buildings and the old network spans 5-10 buildings all in the same campus area. Old network has two core switches currently.

Thanks!