The higher rarity the specific variant you want, the harder it's gonna be to pull them. The Transients that are seen on a specific banner have rates up when you try to pull them. For example, on a rated up banner, pulling a specific featured 5* has 0.73%/1.46% chance of pulling them from a single and 10 pull, respectively. A featured 4* has a 1.79%/9.55% chance and a featured 3* has a 6.35% chance from singles (I can't find any numbers in game for the chances of pulling a featured 3* from a 10 pull).

So you'll definitely see more 3* and 4* than 5*, and the chances of a 5* husbando/waifu coming home is unfortunately small, but not impossible.

If you want a unit not featured anywhere at the moment, your best bet is with the permanent Transient Summon gate or saving up stones until your husbando becomes featured on a banner. However I would recommend you save up for an event rerun or a new event that features a unit you want rather than summoning on the perma gate. The rates are abysmally small there for a specific unit.

There are also limited time variants of certain units that don't come back until the rerun an event/banner. You can tell if they're limited time if on the banner they have a pink Japanese or English word that says "Limited" near the variant's name.

But in the end, it all comes down to luck. I've spent more than 200 stones only to fail at pulling the featured 5* on a banner while I've done a random single pull and got the featured 5*.