What kind of plant are you going to working at? What do they do? Millwright tools differ from factory to factory depending on the machines they have. And there are so many tools to just start out depending on what THEY require you to have and what they supply as shop tools. Everything from sockets, wrenches, screwdrivers, picks, pry bars, tap and die set, hammers of all kinds, punches, drill bits, pliers, allen wrenches, and on and on and on. Just the things I listed above will set you back well over double what your budget is, even buying some used. Then you mention a toolbox, the last mill I worked at supplied a craftsman roll around 42" and made a steel platform with new casters for it.
Your best bet is to call up the company and ask to speak to the head maintenance guy and ask him what your main duties will be the first few weeks and what tools he suggests you bring with you. I know sometimes the newbies will do simple things like press bearings all week long to rebuild a machine. Or replace belts. These things don't require many tools at all besides the shop tools most plants already have.