Unfortunately, wireless units drop signal in crowds. I had issues with those being not as good as expected. Just grab the Sony ECM-XYST1M Stereo Microphone for reliable wedding audio that wont fail...

Checking back on this thread, honestly, if you want to avoid wires and stay within that $300 limit, a wireless system is your best bet for those loud environments. I have been very satisfied using the Sony ECM-W2BT Wireless Microphone with my Alpha setup. Since it uses the Multi Interface shoe, you dont have to mess with any 3.5mm cables. That digital connection is totally worth the money because it eliminates that annoying background hiss you often get with analog inputs. It works well for weddings since you can clip the transmitter right on the officiant or the groom to get clear audio regardless of the wind or noisy kids in the background. For a slightly cheaper alternative that still performs great, the Rode Wireless ME Compact Wireless Microphone is a solid choice. You do lose the cable-free benefit of the Sony shoe, but the internal gain adjustment is pretty foolproof for keeping levels in check. Most of my gear is Sony-native tho, and I have zero complaints about the build quality of their wireless units. Staying under budget is easier if you look for used kits of the Sony ECM-AW4 Bluetooth Wireless Microphone too, but the newer models are much more reliable for range. Avoiding cables really simplifies your workflow when you are rushing between shots during a ceremony... basically makes the whole process less stressful.

Following this thread

Unfortunately, the Rode VideoMic Pro+ Shotgun Microphone is a total hassle with that battery door and the cable always gets in the way. I tried the Sony ECM-B1M Shotgun Microphone and the digital connection is convenient, but the audio quality just wasnt as good as expected for 300 bucks. It feels like you are mostly just paying for the lack of wires.