Bryan has mentioned the Grimdark one page rules a few times as an alternative to 40K, having read the rules they seem to me to almost be a streamlined version of 3rd edition, and I am intrigued to give them a go as a lighter alternative to 8th/9th ed. I personally have found my games of 8th edition to long for what my head says it should be and a bit paralyzed by rules overload (which is in part me not being able to keep them all in my brain).
This link below has everything you need if you are intrigued.
Anyway these rules might give a quicker game, they could yet be rubbish, but I have read them and fancy giving them ago once I have been through my chaos marines ("Havoc Brothers") to find the relevant models.
The rules for play are summarized on one page, special rules on another, then the pre gen (40k esk) list are around 4 pages, with limited special rules in them for force flavor. They can all be downloaded.
The basic Rulebook - start here This will help you understand the pre-gen armies better as it breaks things down in a little more detail that the one page version below.
The core rules and generic special rules - print this as an aid to play This is the one page version of the rules.
If anyone fancies a learning game at some point let me know so we can plan something in (mainly around me having chemo at the moment) and make sure you read the rules.....they are one page