The "being an honest node" argument with just 1-2GH/s is moot, because with such a low hashrate you're probably going to mine on a pool anyways.
In that case it's not you, but the pool-operator who has to be honest (and you don't really have any control about that).
But to answer your question: the cheapest way in terms of initial investment is probably to grab some used ATI GPUs on ebay, although the energy-cost is quite high for the long term. Another way would be to grab some used FPGA boards, higher initial investment, lower energy-costs. Or just wait a few more months and hope for ASICs to be available/affordable.
And that's about all methods around for everybody.