Honestly a good camera phone will get the job done and is within the price range you’re looking for. You can take the photos and save them into a Dropbox app on your phone and access it via your comp. Remote photo buttons for phones are super affordable.

Bluetooth camera shutter remote: CamKix Camera Shutter Remote Control with Bluetooth Wireless Technology - Create Amazing Photos and Videos Hands-Free - Works with Most Smartphones and Tablets (iOS and Android) https://www.amazon.com/dp/B00PJSIIES/ref=cm_sw_r_cp_api_i_FKAR39BVYYHJSK8S9H0X

Phone adaptor for tripod mount: Vastar Smartphone Tripod Adapter Cell Phone Holder Mount Adapter, Fits iPhone, Samsung, and all Phones, Rotates Vertical and Horizontal, Adjustable Clamp https://www.amazon.com/dp/B01L3B5PBI/ref=cm_sw_r_cp_api_i_S2BYD30QF9E8S19K6H6E