Within the next month or so I'm going to be splitting everything into about 8 VLAN's based on departments. Hence there is going to be a lot of inter-subnet traffic, requiring the data to traverse a layer 3 device. The VLAN's will be port based if that matters. The company moves quite a bit of data as they do design and 3d design as well as programming.
I would really question your need to have this many VLANs on a network this small. Unless you have very specific reasons for requiring separate VLANS for each department it sounds like you adding a great deal of complexity without much (perceived) benefit. Sometimes we have to resist to urge to be overly clever.
My plan is to leave the existing switches as distribution layer switches and have them all connect to one layer 3 core switch, each with 10GB fiber, and then have that core switch connected to the router for WAN traffic with 1GB Ethernet. (We don't move too much data over the WAN).
A core switch is a good idea but two core switches are better. In an ideal world all of your network paths would N+1 and this would include the core switch. You can then connect all of your distribution switches to your core switches, and your existing Catalyst 2921 to them. Again, unless you have a specific need for 10Gbps connections between your core switch and your distribution switches - I'd look at spending your $5000 dollars on two smaller switches to fulfill the roll of a network core.
You should also endeavor to link your new office switch directly to the core and not cascade it through an existing distribution switch. Again, this is just good network hygiene. You don't want the loss of one switch to effect all of the switches that are downstream of it.
And finally, unless you very attached to the idea of a core switch, you might be better of not installing a core switch/s and spending that budget on upgrading your existing Netgear switches to something that is fully managed. I realize this sounds like contradictory advice but which option is best is largely dependent on things I don't know, like possibility for future growth, available budget, acceptable network downtime, bandwidth usage, and so on.