The rambling Madman thread is super great, but I get all the information is a bit overwhelming. I'll list parts that I feel like are most useful from the thread for just starting out.
These are things you can pick up regardless of your perk set up:
-Willpower is the stat that's used to determine whether or not a restraint gets applied to you. More willpower means less likely to get restrained.
-Defiance: This is from the Upgrade section. For each 10 current willpower you have over 50, you get +5 to bondage resist. So basically its an upgrade to the willpower stat.
-Willful Struggle: Another pick up from the Upgrade section. For each 10 current willpower you have over 50, you get +1% to struggle power. This is your main upgrade to escaping restraints that's always available. Since you can have up to 400 willpower, this means depending on your current willpower at the time, you can have up to a 35% increase to struggle power. If you've been jailed, your willpower is likely limited, but if your willpower stat is capped, you can still have up to 200 current willpower from sleeping in the bed, which gets you 15% extra struggle power.If you only have the base 100 starting willpower, being jailed would leave you at only 50 willpower from sleeping, which provides no bonuses, so willpower is typically the stat you want to upgrade most often and cap earliest.
-Super Strength: This is a spell in the Elemental Spells category, and is a toggled spell. It can also increase physical damage, but for escape purpose it gives a flat +15 points to your to struggle power
-Unlock: A verbal component spell used to remove a single magic lock. If you're too heavily gagged you can't use it. Of course also costs mana.
-Greater Unlock: An upgraded version of Unlock that removes all magic locks currently on your restraints. Although depending on the version in the past it has also just removed all magic locks on the uppermost accessible layers of restraints. I think the current version does let it unlock it all.
-Disenchant: A Verbal component spell used for dealing with things like magic ropes and belts.
-Release: Another verbal component spell. Using it removes restraints that are currently considered removable (As far as I can tell it just seems to mean restraints that aren't locked). May not effect restraints in an inaccessible layer.
Telekinesis 101: Something not mentioned in ramblings because it can be a tad unreliable at times. It lets you hold a weapon even when bound in a way that wouldn't normally let you hold a weapon. The attack accuracy is 0%, so its typically meant use things like scissors to cut restraints with. But I've found in a fully bound state the character just outright drops it anyways sometimes...and if you have the 'Can't Touch That' perk active, you aren't going to be getting it back that easily.
Next is Goddess reputation. You had your suspicions and you were right. Goddess reputation also effects your struggle power value against restraints. Having good or bad reputation can positively or negatively effect your ability to struggle out of certain restraints. So you want it to go uuuuuuuup. Meaning picking up spell orbs early on better be worth it when your reputation is low. You can increase your reputation with a certain goddess through a handful of ways according to the guide, but I just make sure to do the goddess quests on the floors as I feel I can do it.
Weapons you can use while restrained: Its a good idea to have a backup weapon set in a position to be swapped in if you get bound and can't use your weapons. Arcane Orb and Escort drone can let you still fight back in a bad situation. of course you could always try opting for a unarmed damage build. Then you can deal a lot of damage even in a fully bound state.
For Perks choices, go reread the rambling madman's guide if you want the full gist. I'll just reiterate a few perks that I have a preference for. The Smooth Talker perk for more consistent access to greater unlock and other emergency spellcasting (Like upcasting to incinerate), and psychic to maintaining some access to using items when bound. Quick-draw lets you switch weapons or set up an upcast without using a turn. This is great if you need to quickly upcast to a spell you have access to in order to end the fight more quickly, or need to switch to your Arcane Orb/Escort drone weapon.
As for tactical playing, during the early few floors its a good idea to be really careful until you get your hands on some spell points. Probably don't take spell point orbs unless you have a really good reason to, second guess whether or not you want to open any shadow chests, because they can shoot out some really nasty restraints that are hard to deal with at the beginning. Try to avoid being near groups of enemies. Sometimes the best way to handle groups of enemies early on to just turn around and walk away...and hope you can catch some of them alone later.
Always figure out where your friendly Ghosts are as soon as reasonably possible. I don't personally even open up chests before I know where Ghosts are available nearby, just in case a chest is trapped. As your character unlocks more skills/spells with spell points, you can be a little less careful, but at the early stages always know your escape plan before opening a chest. After you manage to get some willpower upgrades, and some decent amount of spell points invested into resisting/escape bondage, even some tougher restraints like cyber restraints can be struggled out of.
Save up your keys and picks, and keep an eye on your magic key stock, and pick and choose carefully what restraints to actually use it on. But once you feel like you have a bit of surplus, start opening up chests that need magic keys, as they give spell points without angering goddesses.
Take a look at what goddess quests are going to request ahead of time and decide whether or not you feel like you can deal with what you're expecting to spawn. For example, I'm not sure if I can safely handle dealing with the elf and cat dispute at the beginning, but even if I mess up a little bit at the end of a rope kraken fight, I can probably deal with the aftermath.
Its usually a pretty safe idea to explore the entirety of the main part of the current floor before you start exploring your subdivision. The more you know about the layout of the floor, the more easily you can prepare your escape plan if something unexpected happens.
If you need to refill your willpower, and the willpower tablets on the floor aren't really enough to fill it up, you may want to back track to the shoppe floor to be safe. The tables on the shoppe floor will reset every time you leave the shoppe, meaning you can use flipping them to fill up your willpower if more convenient means aren't available.