VIEWPORT SCALES:
You can change the scale you're in by changing into paperspace then going into the modelspace viewport and typing the following:
z (return)
1/20xp (return)
...This will give you a view port scale of 1:20. In your specific case though, the fraction for a 1/4"-1' will be inputted like this:
1/48xp (return)
(ie multiply both sides by 4, to get rid of the 'quarter' aspect and display both in the same units, 12"=1')
It's also worth remembering that it should be represented as a true fraction, so you can't put '0.25/12xp' for example.
LINETYPE SCALES:
The system I have used for displaying linetypes is basic but it's not let me down yet, here it is.
I only use the ACAD.lin file for my linetypes (ignore the ACADISO.lin)
Within this file I don't bother using the linetypes that start with ACAD_ISO... , instead I use just the remaining, ie
CENTER
CENTER2
CENTERX2
HIDDEN
HIDDEN2
HIDDENX2
DASHED
DASHED2
DASHEDX2
...etc.
The linetype variables I use for ALL drawings are:
PSLTSCALE 1
LTSCALE 5
The individual linetype scales of the lines within the drawing are always set to 1.0. I find if you start to play around adjusting the scales individually you'll get some lines showing up and not others. If you haven't quite got the linetype scale/look that you want for a particular line then pick a different linetype ...you have 3 to choose from for each 'type' which is more than enough for most drawings. As a last resort though to get a linetype to show up on a 'short line' I have occasionally changed the individual linetype scale of the line in question to say, 0.9 or 0.8 but I wouldn't do it for a large part of the drawing.
With LTSCALE set to '5' when you go into modelspace (tilemode 1) you'll notice that the lines don't display (since we've set them to display relative to paperspace, PSLTSCALE 1). In order to see the linetypes as they will appear in paperspace we need to change the LTSCALE value temporarily. The calculation is simple: 5 (our prefered LTSCALE display value) x Viewport Scale (that it will be displayed in). So if I was working on a 1:20 viewport it would be 5x20 = LTSCALE 100, 1:50 Viewport becomes 5x50 = LTSCALE 250.
When you come to print off your drawing you must remember to change the LTSCALE back to 5 though, otherwise they aren't going to show up.
The benefit of the PSLTSCALE 1 system means that for Legends/Keys etc you can inport the linetypes you've used in the model drawing into paperspace and they will show up exactly as they do on your main drawing without any adjustments required.
That's it really, simple but effective. There are other ways of doing it and I'm sure you'll get other posts highlighting this, but this works for me all the time ...it's your choice.
Hope that helps
Marc