A Tower Local Controller reported they issued go-around instructions which placed an aircraft below the Minimum Vectoring Altitude.

Narrative

Date and time are estimated. I got asked about the event by Lead which is only way I know about it being an MVA issue. XXL closed and marginal VFR or IFR all day this day. Had several arrivals where insufficient speed control was provided with never going to work overtakes. In this particular case; I was handed a situation where Aircraft X was like less than 3 miles when I got him and decreasing. I quickly asked the operation supervisor to help me scan so we could apply tower visual. After a quick scan I sent him around and what came out of my mouth was Fly Heading 160 climb and maintain 090 which is our standard climb out. I started coordinating and I think he entered the MVA 7500 and 7100 climbing to 090. What I should have said was track the localizer and I didn't. I was worried about getting coordination done and making sure the newer CPC on the other local know what I was doing as he was launching dept at the same time. In these situations; we need more aggressive flow control. I think ZZZ1 does a fantastic job; but it seems like ZZZ/ZZZ1 management is impotent in the fight Person A the Supervisor. They ask for things and he is always lugging the envelope to keep delays down. I think the result of this is ZZZ1 gets oversaturated and has to make some questionable choices as far as sequencing. Please share if needed