It would be easiest to look for rear wheel drive 3.8 equipped Cutlasses, Regals, or any G-Bodies. 1986 and 1987 will have the 109 block but the other 3.8 blocks will be fine for a street car too. This is just for the block; if you need a crank and rods you'll have to find a 4.1 out of a big GM car from 81-84 I believe. They'll have the crank and rods but you could use the bigger block as well. GNTTYPE.ORG has all of this info plus pictures and casting numbers.
The only year of FWD block you might be able to use is from the 1985 A/C/H-body cars. And nobody has confirmed whether that block has the correct motor mount bosses cast into it. The 86 and later blocks use a different front cover so they are difenetly out of the picture. There are tons of 84-87 RWD 3.8's out there so I wouldn't waste my time looking at FWD block.