the omnis started in 85 with the GLH-T version and went to 86 like that. also in 86 they offered the GLHS model which is the numbered 4 door omni only came in Black. the glhs's came with koni adjustables, stock and also a numbered badge with Grounf effects. in 87 the Charger body came out. that is the 2 door version on the omni. also known as the 024. they also came with the 2.2 T2 intercooled motor and came with certain wheels and koni suspension. the best place to look is http://www.turbododge.com. People have gotten them down into the tens easily and there was one that beat a corvette driver at neo nationals 2 years ago.
i have seen an omni be as light as 1800lbs but takes a lot of work and time carving. usually run them around 2300. if i were you i would also look into the shadows. they are great cars and they are the same platform as the omnis just a tad bit more weight and somewhat better looking. Buy Scott Kirks off of him cause he will never get his done. . also if you want there is the spirit R/T which came in only red and white and they were 2.2 turbo cars with lotus cylinder head on them. awesome car. your choice of turbo cars is:
85-86 4 door omni
84-87 Charger (there are a lot converted to turbo cars)
87-89 Shadow (csx-t, csx vnt)
86-93 Daytona (t1,t2,and t4 cars)
87 Lancer/Lebarron body
89-90 Mini Van
your choice pick a car and go from there. ill call around and see what people are selling.