If you are concerned about freezing, then the simplest answer is to install a ball valve inside the house, where it is insulated, so that you can shut off and drain the water before it exist the house.
As for connecting to the sillcock, 1" pex is a slightly unusual size; Most sillcocks are 3/4 inch but 1/2 inch sillcocks are also fairly common, so (probably) what you want is a 1 inch barb to 3/4 inch (reducing) female threaded connector. I found an adapter from sears that could do the trick. U S BRASS CORP/ZURN-QEST QQSFC45GX 1 x 0.75 in. Barb Ringed Shank Pex Adapter. Below is picture of it, but for $17 it's not what I would choose. Also, you would need a 1" ball valve which will cost about $10-$12.
I think that the better solution would be to use a 1" to 3/4" reducer for $2, a 3/4" ball valve for $7 (it's a few $$ cheaper than a 1" ball valve), then a 3/4 inch barb PEX female threaded fitting for about $3. Obvioulsy, you would need some 3/4" pex and some elbows (as Ecnerwal pointed out, the alternative to fittings are bends... 3/4 inch has a tighter radius, but still, if you use a valve inside, then the issue of freezing is mute).
As for making connections with PEX, I like cinch clamps, but a cinch clamp tool is kind of expensive ($40-$120). Shark bite connectors are fickle; sometimes in tight quarters, there's not a better alternative. But I would hesitate to spend so much on shark bite connectors, when for the same price, I could get a new tool (that makes certain connections) which will have paid for itself on the first use (or at least by the very next use/project- over shark bites).