Richard
The banjo head needs to be fairly tight. The plastic heads are VERY tough, so it is difficult to do them damage. If in doubt, slacken off the tension completely and start from scratch.
When I am replacing a banjo head I mark the nuts at the four compass points by clipping a clothes peg to each nut. I then tighten the four nuts (in sequence) by a quarter turn of the wrench. As I move to one nut, I shift the peg to the adjacent nut, so it is now marking the nut to turn on the NEXT circuit of the head.
To get a rough idea of how tight it is flick it with your finger nail. If you get a dull thud, the skin is too slack. If it produces a ringing tone, you are approaching the tension necessary for keeping the banjo in tune. The tension affects how the banjo responds to plucking or striking a string. If it is slacker, the bass strings will be emphasised and the treble end will be more quiet. If too tight, you will not get much bass response at all. Only you can decide where you draw your compromise point.
Once you have got your skin in place, and at the lower end of "tight", fit the bridge in place, locate the strings in the bridge and get it approximately in tune. The bridge should not sink too deeply into the head, although you should see a slight depression where the bridge makes contact. Anything depression much more than about 3/16 inch means that the skin is too slack.
I wouldn't start adjusting the neck angle until you have the drum head tension set (or if you need to get it approximately in position, use a long ruler along the fingerboard, and place the bridge in position without any tension on it. Set the angle so that the ruler passes slightly lower than the top of the bridge.)
This is getting long, so I'll put other suggestions as separate postings.
Quack!
Geoff the Duck.