Metal content to follow under the discone topic (I had to reach to get it in there ;-))
Ground plane first. Just get something working to start with.
J poles are a blast but a bit 'fiddley' as a first antenna in my opinion. That's what makes them a kick to play with.
Do your scanner as a separate antenna for now. (just get something working). A home brewed discone might be fun. but for now, how about another ground plane? A look at a discone will give you any number of ideas on how to get the ground plane elements at the right angle. An indexing jig on an angle table in the drill press would make a nice looking start.
I'm doing a bad thing and not getting involved in the rest of the discussion, but what you need is an antenna you can listen with while you're building the ultimate loaded happy hoohaa bedspring grounded gopher catcher. At least that way you have something to listen to, and compare the results of each of the new antennas with.
When you get your ticket, inverted V if you're on HF, and a ground plane for vhf. You'll find you end up hanging out on mostly the same area of a band, just tune them up, get em running, and build the ultimate wave catcher next weekend. in the mean time, you'll have something that you can listen to.
Humm,,, I guess from my stand point, just get something in the air, even if it's just a long wire into the trees. It's a lot easier to work on an antenna, or other project (even in the lathe) if you've a good receiver running in the back ground.
Now for all the other guys,,, just get something up for now, then as soon as you get your super special rig running you can always take the ratty old thing down.
Did I say just get something working? Good luck, have fun, and it's a hobby,,, it's supposed to be fun!