The cigars I like to have with a beer are the ones I enjoy smoking in general.
There's two things in particular I look for in a cigar ... and if I try a cigar and it has one or both, there is a better chance I'll go and buy more ...
The first is "tooth". Tooth is the formation of tiny pin-head sized oil globules up by the burning end near, and on, the ash of the cigar as it is smoked. This tends to be a richer, fuller smoking tobacco with better mouthfeel (in the smoke) ... though not necessarily stronger tasting.
Another is a distinct "finish". This is where when you get somewhere between 60% and 75% of the way through smoking a cigar, there is a distinct change in the tobacco giving a specifically different taste for the remainder of the smoke. This is from a change in the tobacco at that point in the cigar. A cigar with a distinct finish is rolled that way.
A cigar that is well rolled and burns evenly is also a plus.
I tend to like a shorter cigar such as a Rothschild size, so that I might enjoy a second one with a number of pints in between.
One of my long time favorites is the Punch Rothschild ... I like all versions of the Punch Rothschild but in particular the English Market Selection which is a lighter Colorado Claro ... but I like the darker Maduro and Oscuro in the Punch Rothschild too. Had some Punch Rothschild Oscuros a while back with great tooth. I think the Oscuros are a bit more oily. Great mouthfeel in the smoke.