We typically don't endorse any specific brand of detergent to use. It is best to try what you are currently using, and if you experience any troubles, then go from there. You will want to remember to avoid all fabric softeners and chlorine bleach.
Secondary, if you experience any trouble, you will want to avoid extra things in laundry detergent, like whiteners and brighteners. Things without a fragrance are best. The fewer the ingredients, the least likely to cause a reaction.
Here's some detergents to specifically avoid due to common buildup issues:
All Free & Clear
Here are some that are typically good to use:
Charlie’s (some have reported trouble with this, but I haven't heard of this personally)
Many store brand types, typically have fewer additives, since they add to the cost-
There are many additional good detergents. This is just a few that are common, not a complete list.
Keep in mind that there's more to washing than just the type of detergent. Things like water type, temperature, agitation level, and quantity of water all make a difference.