First thing to check is that your bike can take a 120 axle natively. Coaster brake hubs are sold in a 110-120 configuration, for the most part--anything else, you'll have to disassemble the hub, and put a longer axle in/re-dish the wheel. It can be done, of course, but it is also an impediment to a low-cost build. Make sure you are buying a hub with 14g spoke holes, or use spoke washers, if not (these will add labor for anyone who has ever built with them, beware).

Using a 36-hole hub/rim, you shouldn't need any special spokes. DT Champion, Sapim Leader, Wheelsmith 2.0 spokes, would all be fine. You can split hairs if you want, and buy more expensive spokes (that MAY marginally increase the strength of your build), but they're largely unnecessary, here. You may want to use larger gauge (2.3mm) spokes if you can't source a hub to use 14g...but you will then likely be limited by your rim selection needing larger nipple sockets, or needing to purchase more expensive spokes. Nipples are nothing special, and likely come with the spokes you are buying. DT, Wheelsmith, Sapim...whatever.

Sun CR18s are fine rims for what you want to do, and available in many different drillings.

1300g, with a tire? That's not undoable for a budget build, but strong may be a tall order. I would suggest that you shelve your desire for a light wheel, and build to your other points: durable and strong.