In chess tournaments they try to have like leveled players playing each other in the first round so this would make first round match-ups look like 1v2 3v4 5v6 and 7v8. With losers feeding into the losers bracket and winners advancing to eventually meet the survivor of the losers bracket.
In single elimination tournaments the higher seeds usually play the lower seeds such as 1v8 2v7 3v6 and 4v5. I think most double elimination tournaments follow this format. In the double elimination brackets I created I followed this format and tried to randomize things so players in the losers bracket would be less likely to meet up with the person who put them in the losers bracket in the first place.
Go to my website bracketman.com for pre-printed brackets for 3 to 13 teams. These brackets are in Microsoft Excel and Apple Numbers format and auto-populate the seeds into the bracket as you enter them. It's a free download and requires no registration. Enjoy!