oli gave some really great advice.
For most hunters with a bolt gun you will really be just fine with a single stage press. And a hand primer from Lee, Lyman or RCBS. And a case trimmer. And calipers. All the things previously suggested by oli700.
The dies for bottle necked rifle require case lubing or your case(s) will stick almost permanently in your sizing/decapping die. If you want to lube each case you would be fine with a two-die set that (1) decaps and re-sizes and with the second die (2) seats the bullet. A three die set from Lee includes a case-neck-sizing die that doesn't full-length re-size your brass as long as you are going to shoot your handloads from the same rifle it originally was fired in. If you are shooting the brass over again in your one rifle you just need to size the case neck smaller to hold the bullet firmly. This is the advantage of the Lee 3-die set.
The advantage to doing that is that (1) you don't have to individually lube every case before sizing because it only bumps the shoulder back and sizes the case mouth and neck and it leaves the long case walls alone, and (2) doing this almost eliminates case trimming for the first 5-6 reloads. It is almost effortless to neck-size only with the Lee 3-die set (you don't use the #1 full length sizer doing it this way).
I think the .308 Winchester shines with extruded powders and Hodgdon Varget is a good start. Being a "stick" powder, I agree with oli700 that individually weighing each charge on the scale (which you need anyway) makes sense. You can spend $75 on a powder measure but extruded/stick powders have some variance between each throw because of how the sticks flow thru the measure.
Hodgdon BL-(C)2 is a spherical fine grain powder originally developed for the 7.62mm cartridge and it goes thru a powder measure very consistently if you choose to go with a measure as well as a scale. Ball-See is a pretty good powder for .308 Winchester. It looks exactly like H-335 seen here.
Primers should be whatever you find locally. CCI, Winchester, Federal, Remington.... all good. You should not need magnum rifle primers. And whatever you do, buy at least one bound reloading manual, and don't simply rely on what you can get via the internet. The bound books have a forward section detailing the reloading process far beyond simply knowing that this much powder and this primer and this bullet and this OAL makes a safe load.
