Hi Eskild,
You didn't mention anything about a limited slip differential and thats something you really need to include in your project.
Gear ratios are selected by factoring engine HP & torque curves, rear tire diameters, R&P, desired top speed, and how the car will be used. With that information, you can choose a new 2nd, 3rd, 4th & 5th that will keep the engine in its best powerband and provide a decent top speed.
For durability on the track, you should install a one-piece bearing retaining plate. The stock side cover is more than adequate for a 3.0 engine.
Its difficult to quote costs since the condition of your transmission affects the total costs here. You may need 3-4 syncros, 2 operating sleeves, anchor & stop blocks, maybe a pinion bearing, etc. You just won't know until your gearbox is disassembled and inspected.
I'd be happy to provide the components needed to build a solid, reliable transmission for you, if that helps. As part of that service, I can select gears for you if I have your dyno charts and the rest of the info.