On some rifle/scope combinations, you might run into interference with that rear sight - can not get scope to mount lower without front end of it hitting the sight. Some rear sights fold over to accommodate that - I do not know what you have. Often see scoped rifles with that rear sight removed - not sure if your's is dovetailed or screwed to barrel - dovetail blanks are available; so are plug screws. Leaving the front sight. Again, not sure how your's is mounted. I have a mid 1980's Model 70 in 338 Win Mag. The scope is mounted in the Leupold dual dovetail mounts, so no reasonable way to remove them, without screwdrivers, etc. I rely on my Leupold scopes absolutely, so decided the iron sights served no purpose for me, especially with the dual dovetail mounts, and removed the iron sights - in this case both front and rear sights were attached with screws, so just required 4 plug screws to protect the threads in the holes. On lower powers, can often see the front sight in the scope - often not appearing "lined up" with the cross hair - some people find that annoying and so want the front sight gone.
Mounting height - seems to be a lot about the stock comb height related to the bore line. Quite hard to get a comb height perfect for check weld with iron sights, and then perfect for check weld with a scope. So lower scope height tends to help a bit in those circumstances - but I would say most of my scope hunting rifles are more of "side of jaw" weld, rather than a "check bone" weld. One exception is my Ruger No. 1 in 275 Rigby. Very nice looking express style iron sights, but just no way I can get my fat face down low enough on that comb to use them. But that same comb is absolutely perfect for me to use with the scopes that I have tried on it - very comfortable, fits very well, but only when using a scope.