I usually see two approaches to buying asylum packs.
One is to buy them by cycle. You can either get all six at once, or buy them over time, doesn't matter. The theory here is that cards in the same cycle often are made to work together or use similar mechanics.
The other is to buy packs that have specific cards you want. For instance, when I started I wanted to make a Syndicate/Dark Young deck to take to Gencon. So, I browsed through the deckbuilder on Cardgamedb.com and wrote down cards I thought might work well and what packs they were in. Then, I started buying those specific packs - prioritizing ones that had my most favorite cards or which had more than one card on my list.