It is always better to keep your receiver (ProStick) and Pi indoors, at an easily accessable point. This has following advantages:
(1) You can place your ProStick+Pi in a place which is dry and much cooler than outdoors.
(2) Ease of access to Pi & ProStick. I have to access my Pi several times a month.
(3) No problems of running long length of power feed to Pi.
(4) Pi can be connected to router by wire, no wifi needed. In case you opt for wifi, the wifi signal strength will much better when Pi is indoors, nearer to router.
The only drawback is Coax attenuation. With 35 ft Coax, the coax attenuation is not big even with RG6.
With built-in amplifier of ProStic 35 ft RG6, with two adapters/transitions (N to F ar antenna, F to SMA at ProStick), should be ok. The connector outdoor should be wrapped in self-fusing/self-amalgamating tape to protect ingress of rain water & moisture.
However if you feel uneasy/non-confident about attenuation of RG6 and/or adapters at both ends of coax, go for pre-made LMR240 or LMR400 with N male at one end and SMA male at the other end. This will be somewhat costlier, but will give you peace of mind.