When farming for characters, there are a few ways to go about this. With the inclusion of soul fragments for increased soul levels from opening lower level souls, the options have increased.
Achievements and missions
A lot of unique characters require you to do missions or earn them through an achievement. These are pretty useful as you go and can unlock some segments of the game for you. Grim Reaper Eddie for example was my gateway to BNW. Other specific characters are appearing lately due to the Frontier Keys Dungeons achievements. This way of earning characters has one definitive advantage, you don't rely on RNG to get the one you want, only time and dedication...
Lord Of Light
The first approach is to play LoL dungeons. Yes, this also allows you to farm for some evo materials and complete some of the events, but you'll quickly find that you can amass hundreds or even thousands of souls by farming LoL. While the number of rare or better is going to remain small, the common souls in bulk can make up for it as you open stack after stack to either sell or sacrifice, which will in turn earn rare souls. Speaking of sacrifice...
It seems counter-intuitive to think that sacrificing characters is a way to farm characters, but relieving yourself of duplicates is certainly rewarding in the number of sands of time, evo and upgrade materials, as well as higher level souls. As your level of sacrifice increases, the likelihood that you'll drop a rare soul, a colored class rare soul, an epic or even a legendary soul increases. Filling the vortex has been a great source of legendary souls, and the bonus of fragments of The Alchemist are well worth the effort. While it may seem like it takes a long time for that first vortex fill, they will start becoming more regular as you move along in the game.
Usually once per month, there is a LoL event which gives out fragments for the latest 4* character. While this may not seem all that exciting, it can add that one new character and give you excess fragments to either spend in the store as a form of currency (recent trend) or you can get extra 4* characters for a future sacrifice... see above. Also, these events usually give out Lilith soul fragments, and you're going to eventually want all of the Lilith characters on your roster. Duplicates can again be sacrificed as well.
Other events reward you with souls as well. Keep an eye on your newsfeed for details about those events and watch for souls as rewards.
Remember when we said not to spend all your ironite right away? Well, 100 ironite will get you a rare soul, and 900 will get you 10 of them. If you're early on, building up your team is going to require a lot of souls, so grabbing a 10 pack here and there isn't totally frowned upon in most circles.
Frontier coins are another form of currency in the game. Farming frontier coins essentially means playing events, gauntlet, and sometimes arena - watch your newsfeeed - but becomes a valuable resource for gathering souls. If you look in the store under "Frontier", you'll see Angel and Gambler, Killer Prime, Ferryman, The Beast, Alexander Eddie, the Eternals, the Gods, and the Liliths in there, all just the click of a button (and the frontier coins) away from being yours. Keep saving for the higher level ones and you'll find that you can farm more frontier coins quicker once you start opening up the more expensive ones. Mythical souls are also available for frontier coins.
Playing arena and gauntlet for souls? Sounds silly, but you can buy souls for iron coins. Legendary souls, rare souls, warrior souls, sentinel souls and magus souls are limited to how many you can purchase per moth from iron coins, and you're going to want to buy more relics than souls, but they are indeed available this way.
When you rent something, it typically costs you. In this game, you AND the player you rented a trooper from get a bonus. How generous of them. By playing all of your troopers daily (an increasing number of slots available as you progress through the game, with the max currently being 50), you get 25 trooper badges for each one. In the trooper store, you can buy rare, warrior, magus, sentinel, common, gunner/assassin common and rare gunner/assassin souls. Each type is limited to one per week, but it's a perfectly good place to pick up some new characters as well as grabbing some skill shards and fragments of a trooper soul, which will give you another 5* character. You can also grab fragments for a precious soul here, which doesn't necessarily give you more characters to play with, but it will give you more sacrificial hearts and / or golden idols to get some gold.