I generally run the numbers via USPS Priority and UPS when I sell a gun. Sometimes they are close to the same, majority of times UPS is cheaper.
I ship from home using a personal UPS account. Signing up for one is free. When shipping from home, one can use the UPS discount codes, which you won't get if you just take it to The UPS Store and have them do the shipping. For example, a current UPS discount code is 'easy' and it gets you 10% off. Once you generate the shipment and print the label at home, you can schedule a UPS pick up (costs extra, how much depends on whether you are 'in town' or out in a rural area like me), or you can just drop it off at a UPS Store location (you won't have to pay any of their surcharges if you have already printed and paid for the shipping at home), or any other UPS location. Beware that UPS Store locations generally do not accept 'high value' items (insured for over $1,000), so you will not have that drop-off option.
The UPS main web site has a simple 'Calculate Time and Cost' page, where you just have to put in the to-and-from city & zip code info, box weight, box dimensions and insured value. FX guns are generally a little more to ship since you are also shipping the weight of the hard case, but most air rifles require a longer, larger dimension shipping carton, so you will likely be charged based on 'dimensional weight' as opposed to actual weight. But on the plus side, the guns are very well protected from shipping damage in their hard cases.
Link to UPS Calculate Time and Cost page:
https://wwwapps.ups.com/ctc/request?loc=en_US Some locations (Hawaii and PR, in my experience) virtually mandate shipping via USPS as UPS gets really expensive to those locations.