I'm curious what Instrument Rated members of this group use for
personal minimums for takeoff and landing for single engine aircraft.

The question is prompted by a recent flight where the takeoff
conditions were 200 ft + 1 mile. That's lower than I've ever done
before, and it occurred to me that if I had any significant engine
problems, it was all over unless I was extremly lucky.

Aim at worst case without using your luck.

What counts are the "way-out" options: What to do with an inflight
problem (anything better as an engine failure) after take-off? Can you
do the go-around-procedure? What are the minimums now for a landing at
your "new destination-welcome-home" airport?

What do you do enroute with an engine failure? Hopefully your are high
enough to navigate, decide and communicate. You better have some VFR
below, to avoid trees and cumulus grantitus during your perfect
500ft/min one-way descend.

At the destination you want to see the runway early enough to fit your
personal experience and capability.
The legal CAT I conditions (200 ft, 550 m) are something special!

Personally I got my IFR Ticket last year, so I set my personal minimus
rather high for the beginning. I seek for a "way out" under all
conditions: Such as suitable VFR below and 1000 ft at the destination.
Maybe at a later stage I would reduce the 1000ft to NON-PREC.
conditions.

I did not dare to deal with the legal CATI options (PREC. APR.) but
tried losy weather in a simulator. Try to see the approach lights in
550m yourself with a 200ft ceiling! MS Flight simulator is absolutely
sufficient for this impression.