While crossfire does yield better performance scaling than SLI does, it tends to come with headaches and is only supported in applications that have a pre-defined profile set by AMD.
Pros: Possible performance increase if its implemented well enough on the driver end. Fallback dGPU in the event of a single card failure. 2nd dGPU for passing to VMs. In applications that support it, you can actually reduce the stress on a single card and split the load across two = prolonged life of the hardware.
Cons: Support is limited, and doesnt always yield ideal performance gains. Heavily increased power consumption. More steps to get setup and optimized than is ideal. Chance of odd behavior just because, those things tend to happen when you're slaving a GPU to another. Heat. AMD cards are fucking hot, it's no secret. Without water cooling your cards, you're going to severely limit yourself because of thermal levels. VRM throttling is abundant.
Generally speaking I would say that unless you have an actual need for two cards right out of the gate, it's not worth the extra money invested, or the hassle involved. Stick with the standard advice of "Best card you can afford now, expand later on."
I've been running multi-gpu setups for years, dual and triple water cooled gpu's. It is more of a hassle than a single card setup but I still have better performance than any single card can achieve. I have a 4K display and before that I was gaming with 1440p @ 118hz so I could make use of the extra grunt from multiple gpu's. A single R9 390 should be more than enough for a single 1080p display with most games maxed out and probably be able to drive a triple 1080p setup decently since it has 8 gb of vram. Some of the settings may need to be lowered though. You can always pick a used one later on off eBay on the cheap. It makes the price/performance a little better since you might not always be able to utilized multiple gpu's. I'm running 3 R9 290's now but most games don't make any use of the 3rd card but I got the 3rd card used for about half price of a new one. Water cooling is essential for R9 290/390 other wise thermal throttling would be a real issue unless you can deal with the fans running at about 80% to 90% under load. Under water, they stay between 60C & 65C instead of hitting the 95C thermal limit.