Ohhh sorry I missed your point about price.

Shave cream and brush for $10-15 will be tough... but you can do it for about $20.

Couple cream options ($10 or less):

Palmolive For Men Classic Palm Extract Shave Cream 100ml https://www.amazon.com/dp/B0012Y1ELM/ref=cm_sw_r_cp_api_i_6sBwCb19FTMJ9

Old Spice Shave Cream - 70 g (Original) - Pack of 2 https://www.amazon.com/dp/000004458X/ref=cm_sw_r_cp_api_i_CvBwCbQZ9ART0

C.O. Bigelow Premium Shave Cream with Eucalyptus Oil 147g/5.2oz https://www.amazon.com/dp/B002O7UI18/ref=cm_sw_r_cp_api_i_DwBwCbW9Q5RHD

Proraso Shaving Cream, Refreshing and Toning, 5.2 oz https://www.amazon.com/dp/B00837ZOI0/ref=cm_sw_r_cp_api_i_hxBwCbMNJSWK1

And this is a perfectly good starter brush for $10:

The Body Shop Men's Wooden Shaving Brush https://www.amazon.com/dp/B001PDDEVS/ref=cm_sw_r_cp_api_i_CyBwCb3YSDEH8