The savings part depends a lot on what you load. When I started a few years back I got a progressive for 223 and pistol and a single stage for rifle/precision. I have found I use the single stage WAY more often. Two reasons:
#1. When there is not ammo hysteria, loading fmj 223 or 9mm saves a little bit of $, and gives you better consistency. But, factoring in time and the fact that if I want to load a lot of something I generally don't need absolute precision, there is less value.
#2. For bolt actions, you can really tailor a load to a particular rifle. You can be extremely precise in powder loads and seating depths. Value wise, you can typically load high-end bullets for around the price of the cheap factory ammo, and for significant savings over high end factory ammo. This is especially true in the larger and less common calibers. I forget my exact math so don't call me out, but I figured I could load a box of 300WSM with Nosler ABs or Barnes TTSX in the low $20's, while a box of premium factory ammo is north of $50. Plus, mine are tailored to my exact rifle, from headspace to bullet depth. Pride and results!
Read as much as you can before getting started and check out product reviews from posters here and at Accurate Reloading. It is a great hobby and you can match your approach to your level of interest. Measure everything twice and load safe!