I'm going to use a FreeBSD system as a loadbalancer which routes 1gbps public traffic to back-end webserver cluster. What are the minimum hardware specs for this job?
The minimum hardware specs for load-balancing 1gbps of web traffic is ... irrelevant. If you put the smallest hardware in there, and you experience even a small denial of service attack, the machine will likely be so busy that it's impossible to respond to the attack.
My experience has been that I want to put pretty much the most powerful box in there that I can. For example, one I'm running a Core i5 3.5GHz dual core CPU...
It really depends on what kind of load-balancing you are doing. If it's simply kernel-level IPVS, that's going to require much less horsepower than doing something like HAProxy. And then it depends on what exact configuration of HAProxy, how many regexes you are applying to the requests, etc...
So, while you may still want to figure out the minimum hardware, I'd recommend that you seriously over-provision the box.
If it is not going to do SSL decryption almost any piece of hardware built in the last 5 years will be able to saturate a GB NIC. Stick with something new enough you trust its reliability since this is a pretty critical piece of hardware.
As Sean mentioned it would be dependent on the type of Load balancer you use.
Layer 7 load balancers like HA-Proxy are typically more CPU hungry because the load balancer kind of partially processes a request before handing it over to the backend. They are similar to rever proxies.
Layer 4 load balancers. I personally like this. At my previous work place we handled Gbps traffic with a single dual core xeon. That was the cheapest one available. The only requirement was RAM. We were using 4Gb of RAM out of which 50% of which was not used most of the time.
This link will help you understand the different types of loadbalancers http://www.loadbalancing.org/#Layer-4_Load_Balancing_