Welcome to FlyerTalk, brooks.7.

Chances are the best prices (in either of those cabins) are going to be with out-of-the-way routings and/or on obscure carriers you've never heard of.

But you can find all that simply by using some many airline search engine like Kayak. There are no tips on lowering the prices you'll find form a many-airline search engine, just on not restricting yourself to simple/direct routings and not avoiding airlines that you've heard of if you're interested in saving money.

The other possibility is looking for "flash" sales, but by their very definition they're only around for a short time, and not dependable (and I don't know of one place that keeps track of all of them). Qatar Airlines just had one a while back, but it's gone by now.

Or using miles. Miles availability tends to be best in many case when booking 11-12 months out, which is roughly where you are right now. But if you don't yet have (enough) miles, that won't help much, because it'll take quite some time.