Pantherart, If the mesh is metal (Photoetched), you only really have one option, and that is superglue (although epoxy would work too). If plastic, you can try 'normal' liquid glue but it might not give you a strong joint.. Superglue would be the type of glue I'd use...
You'll probably find easier to paint the tank and the mesh separately, and do a final assembly just before applying the last touches of your weathering (such as pastel chalk dust). Decaling, washes and dry-brushing should be done prior final assembly, to make things easier and limit the chances of breaking things...
Superglue might give you a few shiny spots. Let the glue dry then 'cover' the shiny spots with a touch of paint/weathering.
Hope this helps!