The weight penalty of a 3rd gen sedan (DB7 / DB8) is minimal compared to the coupe (DC2 / DC4) Both the sedans and coupes look great IMO.
To hit 300 at the wheels, I'd actually start with an LS or GS model. GSR sedans are comparatively rare; they command a higher price on the used market (unless you find a chump to exploit). Non-VTEC sedans and coupes are available for reasonable money..and since you'll be tearing down the motor anyway, ultra high-mileage cars may save you money up front.
Regardless of which motor you boost, forged internals (rods,pistons) will be mandatory. Your crank will be fine. While you're at it, a cylinder bore brace ought to be installed to strenghten the cylinder bores.
Chassis wise, I'd look into polyurethane bushings in a few areas, working in concert with an upgrade in springs and shocks. Koni Yellows and Ground Control sleeves are a popular solution. Obviously, an upgraded clutch, a limited-slip differential, and strenghtened driveshafts will be needed to get the power to the ground. For the non-VTEC heads, a quick port-and polish together with a set of Crower 402 (turbo) cams, valvesprings and retainers will do nicely.
Brakes: IMO, with 300hp worth of go, you're going to need about 1200hp worth of stop to be safe. So I'd include some form of brake upgrade, ranging from larger rotors, to a whole new setup with larger calipers and upgraded lines.
The fiscal impact is clear: Building a 300wheel hp 4-cylinder motor that is as relaible as it's stock 120 wheel hp costs serious money. I could see this project costing six or seven thousand dollars on top of the cost of the vehicle.
I'm not trying to discourage you, in fact I think it'd be great to see a DB sleeper that can rape Corvettes..

Just be thorough and balanced in your mods, and never compromise on safety. I for one don't want to hear of someone killing themselves by stuffing a monster motor into an underprepared chassis.