Help in chosing Mosfet
The MOS part is not difficult, any MOSFET which can withstand the voltage and current will do but you have underestimated the problem. Just controlling the gate will yeild very unpredictable results and no regulation so this will be difficult.

Best option is op-amp and current feedback but if you want to keep it open loop and simple, an BJT instead of FET with suitable beta and base resistor will give you far more control.

BJT, slightly better than FET solution but still plenty of drift and no regulation:






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One possible opamp-solution, 12 V supply:






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5 V only equivalent:







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