I load 6.5 CM for roughly $1.10 per round using match components, so 308 I could see being similar. Easy to price out your bullet, powder, and primer and about 10ish times to use average pc of brass as a quick check to what it would cost you before your time, and equipment. Then factor in the equipment you would need. Press, dies, scale, etc as fixed costs to recoup in the savings. You don't need all the tools to start getting good ammo, and you can slowly grow from the min requirements. Garvin, Ultimate reloader on the tube has great video's with press comparisons, and on the reloading processes as well. Great way to start.
You do need to shoot a bit before seeing any actual returns if you are just starting out, but it is doable depending on the amount you shoot. I tripled or quadrupled my shooting amount since reloading, but it is something I enjoy, and have time to tinker on the press. With already prepped brass, you will need about an hour to reload 50 rounds on a single press, beam scale, so factor that.
The 308 you can get brass with small rifle primer pockets, and that would be the way to go. Primers and availability is the biggest issue right now, with the small rifle primers easier to find and more plentiful still. Lapua makes the SR, "palma" brass, but I don't know of availability as I don't shoot 308. Starline, Alpha, Peterson should make SR brass as well.
Pistol primers are still fairly easy to get as well, 44 mag, 38 spec if you have those.
You can look at Hodgdon load data site to see comparable powders to the bullets weights, to get an idea of amounts of powders, and types you can use. 7000 grains roughly to a lb, so you can easily factor powder per round costs that way.
400 rounds per month is worth it to reload for and see savings eventually after the tools purchases. Bonus is you get to "tune" your ammo to your rifle and play with numerable variances to dial things in.
Rough price, I didn't look into specifics, and more of a layout.
Bullet: 167 gr lapua scenar: $649/1000; so $0.65 per.
powder: Varget. 44.5 grains. Book calls for 45 gr max. $75/ lb, so roughly 157 rounds or $0.48 each.
brass: lapua $139/ 100 pcs. $1.39 each pc by 10 reloads is $0.14 each reload.
primer: Fed 205 small rifle match; $190/ 1000: $0.19 each.
So quick math puts you $1.46 per round, plus your time, plus all the equipment to reload.
$1000-$1500 would get you a good budget to get set up with "good" equipment, so after roughly 700-1000 rounds you have saved to pay for the "start" up equipment. We know it never ends there, as there are rabbit holes to run down and things to always add to the "kits" to make it easier, more accurate, quicker at reloading.
Now depending on the factory bullet you shoot now, sometimes they do show the powder that they use, so that is a start as well, and you could always pull one and weight the amount of powder in there to get you a rough start, and fine tune from there.
So a quick short answer is you better get going on learning what to purchase and how to reload, as yea you would save in the short term!! Welcome to the rabbit hole!!
Me, I did a bunch of research ahead of time and purchased "better" equipment from the start, and not any of the available kits. Forster press, RCBS M1000 beam scale, whidden dies, just to name a few. Are they necessary for match ammo, no, but I know they are better than some of the rest. Can you load match ammo with others, RCBS, LEE, Redding, etc, yes. Just watch a few "Ultimate Reloader" vids and decide yourself what you want to spend on.