Hi Brian,
For general woodworking use, use an Aliphatic glue. It sets quickly, dries clear, is effectively waterproof and is water clean up. There are a number of different brands on the market but you can see more details on the DeLuxe Materials website **LINK** which has lots of useful information. Also their Super Phatic glue is the water based equivalent of superglue.
You will need to seal your model when built before painting it. For this there are several options available including cellulose dope, sanding sealer, resin or the new EzeCote from Deluxe Materials which a number of people on this Forum have found very useful, including myself.
Colin