I want to mount a Leupold 3-9x36 Mark 4 MR/T 30mm scope (Illuminated Mil-Dot, M3 Target Knobs) on my standard 20" AR-15 rifle (has YHM 2-piece non-FF handguards).  

The rifle has a FSB and I'm not sure if this will be a problem or not (will it get in the sight picture?  If so, will this be a problem?)

What type of rings/mounting system should I look at?  When I use Leupold's Mount Guide, it tells me there are no base/rings available for that combination of scope and rifle.

Also, I might want to be able to move this scope back and forth between the AR and a Winchester Model 70 that has Baer Custom tactical mounts on it.  Is this doable?  Is it practical?  What height rings would I need, and could I use the same set on both rifles?  Leupold QRW?  How tall?

I'd also like to have room for a rear BUIS.

Thanks in advance for your help.

You could use the A.R.M.S. #22 high rings or the LaRue Tactical SPR 1.5 for mounting on the AR.  I have used both with the scope you mention (except mine doesn't have the illumination) and prefer the LaRue in this instance as it gives you more leeway for eye relief.  

The front sight base should not be a problem with this set-up.  At the lowest setting of 3X the front sight appears as an aberration in the lower half of the field of view that doesn't interfere with your aiming point.  At higher settings I hardly even notice it.  As you can see from the picture below the LaRue gives plenty of clearance for a BUIS.

Quoted: Also, I might want to be able to move this scope back and forth between the AR and a Winchester Model 70 that has Baer Custom tactical mounts on it.  Is this doable?  Is it practical?  What height rings would I need, and could I use the same set on both rifles?  Leupold QRW?  How tall? I'd also like to have room for a rear BUIS. Thanks in advance for your help.

Get a GG&G Scout FIRE rail that basically elevates your mounting surface and extends it over your handguards a little.  Then get some Medium-height tactical rings from TPS or similar and mount the scope in the rings so that you will be able to place them on both rifles and get proper eye relief by choosing slots.

As long as the slot spacing on your Baer mount is up to the same spec as the GG&G, all you would have to do is unbolt the rings/scope assembly from the base and drop it on the other gun.  Figure out/write down the changes needed for rezeroing and go for it.  This is practical if you are only going to swap occasionally --- otherwise just get dedicated scopes.  Every once in a while the Leupold PR 3-9x with the target turrets shows up cheap on the EE....

You might be able to see the FSB in the lower part of your view at lower powers.

+1 for the Larue Tactical SPR 1.5.