I am going to need ~10-12 gigabit cards, so obviously, I don't want to spend more than I have to.
Shop around then, there are great variations in prices. You should consider the underlying chipset more so than the brand name, and digging that up often just means looking closely at the picture, and sometimes downloading the driver and examining it.
In gigabit, there are a limited number of chipset providers. E.g. Intel, Marvell, Realtek, VIA, and Broadcom. Intel are generally considered the best, and also tend to be the most expensive. You can however sometimes find good deals for used Intel NICs on eBay -- typically old server pulls. Of course, you'd have to be careful with eBay purchases, research the particular device (avoid fibre NICs look for current driver support), and be willing to take some risk.
If you take a "I want quality, and I'm willing to pay for it", Intel is an easy answer.
If you take a "I want gigabit at the lowest cost possible", then you're probably looking at VIA or Realtek chipsets unless you luck out on eBay. I have no experience with VIA NICs, but Realtek has passable driver support and performance, although at a relatively high CPU utilization. Marvell PCI is better on CPU utilization, but this comes with generally less throughput.
How much will this matter? Probably not that much. Getting to gigabit alone is the big step. Fine tuning gigabit for the best possible performance is generally an exercise in frustration as some non-trivial, hidden and uncontrollable factors come into play. (E.g. OS performance, PCI bus performance, composite of issues on both ends of the transfer.)
Are on board gig-eth adapters usually connected through the pci-e bus or the pci bus?
Both. Many still hack something on the PCI bus, many use a newer PCIe chip. Some have both. You can usually determine this from the model number of the chip, if the motherboard vendor doesn't tell you up-front or provide a system diagram with that information. Some motherboard vendors have even disabled or crippled a nice native NIC and hacked on a PCI-bridged one (e.g. Gigabyte has done this at times).
IMO, PCIe versions are generally worth pursuing when possible, not just for the bus issue, but also because sometimes the PCI versions are ancient creaking designs, and the PCIe versions perform better. Of course, this is also a simple generalization -- sometimes vendors have gone in the opposite direction, from older well-performing NICs to cheaper ones later with smaller feature sets and potentially less performance.
The good news is that all these details for the most part don't matter much for simple workstation usage -- the bottlenecks are elsewhere.