I wouldn't wash the top at all until it's quilted and bound. The seam allowances fray on the back, seams come undone and the fabric could shrink at hugely different rates when it gets wet, leaving you with a quilt top that is unmanageable.
I've bought a lot of old tops on eBay and they've all come out much nicer than I could have expected from their age and condition.
All of them were very hard to quilt - none of them were square and flat and one of them nearly caused me to lose my mind - it was a Drunkard's Path in brown and peach and had apparently been pieced by at least two people with vastly differing skill levels.
A couple of these tops have been badly stained and watermarked and stunk to high heaven of mildew and who-knows-what.
I use fusible batts for these troublesome tops - they really help you get the quilt under control, but the requirement to iron it to the batt may set stains even more stubbornly.
I usually quilt these old tops pretty heavily so that the batt and backing supports the old fabric well. After quilting and binding, I wash in hot water and dry in a hot dryer. Because I want the recipients to be able to use the quilt, I want to give it the harshest treatment that it's likely to face in the future to make sure that it will stand up to that kind of treatment.
I use detergent, OxyClean, Color Catchers and about a cup of ammonia in the wash water - so far this has removed almost all stains and yellowing and the ammonia strips out any odor.
After laundering, I inspect the quilt on both sides and tie off loose threads, darn or patch any spots of fabric which have shredded in the wash, etc.
I'm not necessarily recommending that you do any of this - this is just what I do.
But I have little of value invested in these quilts and they're ordinary, run-of-the-mill scrap tops I'm talking about.
If the top is pre-1920's or if it had a large sentimental or monetary value, I'm not sure I'd even touch it, much less treat it like a top I made. :)
Drunkard's Path - quilted with big roses in variegated peach and vines, leaves & tendrils in rust - this quilt stunk so bad I could barely stand to handle it
Scrap Quilt - quilted with feathers - badly water stained and smelled of mildew, but it's fresh and bright after laundering
Grandmother's Flower Garden - heavily quilted with fans, flowers, vines and leaves