It's really up to you which shipping option you use within the US - there aren't the same shipping issues with mailing it to NYC than there are with mailing a spousal visa to Sheffield.
However, personally I wouldn't recommend using USPS as it's less reliable than the couriers like DHL and UPS, but as it won't be leaving the US, you don't have to worry about things like customs and international tracking (which can be a problem with international USPS shipping).
My recommendation would be overnight/next day shipping with either UPS or DHL. I'm not sure if the issue with FedEx is only for Sheffield applications or all applications (I know there were issues with international return shipping from Sheffield with FedEx).
The VFS Global shipping service is nothing more than pre-paid, fixed-price UPS shipping, so it's worth checking the price with UPS first to see if doing it yourself would be cheaper. As you're only shipping within the US, you may be able to sort out a pre-paid return shipping label with UPS/DHL yourself.