I think $125 is doable, if you are comfortable shopping online. If you want road pedals (3 bolt, non-walkable), the Shimano R540 are a solid but heavy entry level model. You can sometimes find very good deals on them from bike retailers, ebay, etc., and you should be able to obtain a pair for ~$40 or less. I got a new pair for $6 once, but that was a very odd deal.
Buying shoes in person will probably be more expensive. If you go the online route, Amazon is very good about returns (if you make sure you purchase through Amazon itself and not a third-party seller). The nice thing about being an odd size (I'm at the other end of the spectrum, FWIW) is that products in extremely large or small sizes are often priced lower. Do a bit of research regarding shoe widths (some brands are known for running narrow or wide, large or small) and you can probably nail online shopping for shoes.