Weather/environment sealed connectors, buttons? Sealing an LCD display at the edges?
First you should take a look at the IP Code and decide the level of protection you desire. The IP Code rates enclosures, connectors, switches etc in terms of their ability to survive in harsh environments including water. In the marine (boats) environment a rating of IP67 is often specified, but that is probably overkill for your application.

Once you know the IP rating you want you can then select a connector that meets that rating. One type of cabling you might consider is Ethernet cable if it has enough wires to meet your needs. IP67 Ethernet connectors are readily available. Here are some, but shop around as I am sure you can find much better pricing.

Here are some IP67 pushbutton switches. 

As far as the LCD goes, why not just use a box with a clear plastic front and mount the LCD inside the box? For something cheap you may be able to use a standard plastic electrical box from Lowes or Home depot such as this (they come in various sizes). Instead of the standard cover plate, just cut one from clear plastic.

As far as humidity getting into the box, there is a reliable way to prevent this, but it would probably be way overkill for your application. I simply describe it here in case someone else reading this question has more stringent requirements. The box can be filled with an inert gas like nitrogen under pressure. This will prevent the ingress of moisture.