How to decide PCB specification
The material to use for the PCB (difference between FR TG 130, FR TG170, Aluminium, or other mateials)


Use the lowest cost material that meets your needs. If you don't have special needs, this is typically FR4 (there are even lower cost materials for truly mass-market products). Higher Tg might be desirable if you are doing lead-free assembly (unfortunately I can't give specifics here).


  PCB Thickniess


If you don't have a specific reason to do otherwise, use 1.6 mm (63 mil). This will give reasonable mechanical rigidity and compatibility with the maximum number of through-hole parts.

If you have a very high layer count (more than 16 layers, maybe) you might need to go thicker. 

If you are trying to fit certain edge-card connectors you might need to go thinner (1 mm is not uncommon).


  Surface finishing (when to use HASL vs ENIG, vs OSP vs Gold or vs Immersion tin)


Use the cheapest finish that meets your needs. Typically this is HASL.

Gold finish may be desirable if you are using edge-card connectors or otherwise using the copper surface as a switch contact, or if you are wirebonding to PCB pads.


  Copper weight (1,2,3,4 oz)


Use the cheapest that meets your needs.

Typically this is 1/2 or 1 oz. 1/2 oz may be preferred on outer layers to allow finer features; after copper plating it will be roughly equivalent to 1 oz unplated copper in current-handling capability.

Thicker copper may be needed if your circuit must handle very high currents.