for more privacy/ anonymity would you be better of building your own computer instead of buying a laptop lets say, straight out of bestbuy?
If you referring to the risk of backdoor-ed hardware and interdiction then probably yes building from parts would be lower risk.
But what your looking for is open source hardware to really reduce the risk.
This is an example of hardware that is almost fully opensource.
Ben NanoNote – handheld notebook computer based on a MIPS processor running Linux.
Chumby - “Ambient” information device.
CUBIT (multi-touch) System – Open-source multitouch surface-interaction system.
EOMA68 low-power modular computer.
Novena - Open-source Linux computer based on a 1.2 GHz (quad-core) ARM Cortex-A9 and Xilinx FPGA.
Open Compute Project – Openly share designs of data center products (server, storage, rack, …).
Parallax Propeller – a multi-core microcontroller with eight 32-bit RISC cores.
Parallella - an opensourced Single board computer featuring a Manycore coprocessor and an FPGA.