You can get gently used 2013 T420 Thinkpads on eBay for around $150 with an i7 processor, NVIDIA dedicated graphics, and 4GB of RAM. For non-gaming, it's just not worth it to go anywhere beyond that.
[0] https://forums.lenovo.com/t5/ThinkPad-T400-T500-and-newer-T/...
[1] http://pcpartpicker.com/products/memory/#t=9&Z=16384002&s=30...