Back in 2013/14 I bought two memberships and was able to get 4 tickets under each account in the "neutral" section. The section was all Reds, most wearing colours. Back then we didn't need any previous credits, but it was a midweek evening fixture and times have changed now.
This season (very fortunately) the Mrs's boss wanted to see Fulham on Boxing Day, so we already have some credits. But Swoopy's tip below should also work.
The Spurs selling criteria suggest that (a max of 4) tickets will go on sale to Members first, then Season Ticket holders, then people who have a purchase history. It wouldn't surprise me if they preempt a big interest for Liverpool and stick in an extra round of "Members with history" first.