From the sounds of it your looking to do something that more like the suits worn in CATS the Broadway show.

If you notice they managed to put fur on the suit but did so only on the shoulders and just around the bust line, and panted the rest of the body suit to look like it was furry.
This is a good place to start if your looking for form fitting. You could still make a Fur Suit "mascot" like head give in the fur on the shoulders is there to blend your head into the rest of the costume. There is also the option of making the gloves and paws that you see in most partial costumes. Do note that the rope around the actors waist in the picture above is how they put the tails on their costumes. You could do this or something more creative to make it seem more apart of you than just tied on.
As for tacking fur onto a body suit? I would think the best way to do so is to get a VERY skilled and trusted person to hand sew the fur into place while you have the suit on. Pokie hazards might draw you away from this idea but its the best way to ensure your fur won't be too tight in areas or bag when you put your suit on. The other option you have to put the fur on to the suit is Fabric glue. You would still need to wear the suit while doing this option as well to keep the fur form fitted and to keep the glue from adhering to your skin you could put all the fur on and then rub off the excess that bleeds through the fabric onto your skin.
also a few under garment ideas to make the body suit flush and not looking like you have under garments on is to wear seamless style panties and silicone nipple cover. which is a ultra thin matte silicone for undetectable coverage.
Hope this helps (:<