WRT gods:
1. Valpurus and Mortifer can only be prayed to once you are considered their champion. Praying to them without any alignment training/god-specific sucking-up at all tends to result in instant death. In the event you do pull that off, Valpurus will give you either a two-handed valpurium sword or a valpurium shield while Mortifer will give you Neerc Se'ulb, as well as maybe a pet angel. Prayer cooldown period for both of them have been clocked as around 50 hours vs. the 3 for other gods, so their help is limited even more than the nature of their gifts would suggest (although in order to get the best possible ending, you must be Valpurus' champion on top of possessing Petrus' left nut and having the Shirt of the Golden Eagle - good luck with slaying Petrus and Oree for those, though). As for your actual question, I believe I recall someone claiming that there was some kind of spread you could work with along the lines that you could have three gods more lawful and three gods more chaotic with one in the middle or something like that without having any negative god relations through prayer, but I don't recall it that well, so I'll just say that in the event you were going to revolve around Valpurus or Mortifer that you'd want to avoid praying to any god that was L- or more chaotic/C+ or more lawful (you can't revolve around that, of course, since the most benefit you can realistically get out of Valp or Morty is two prays for a sword and shield or dual Neercs, but we're going with hypotheticals here).
2. I never quite liked dealing a lot with gods; mostly because it seemed to me that the sanest way to train intelligence (by reading every book I could find) was also the worst way to handle god relations and I really wanted to get smarter faster so that better materials would be available for changing my stuff into sooner and give me the life-extension I'd need to win. But of course, by ignoring the gods I often got dead anyway. Since I'm not really going to be much help in the "lawful vs. chaotic" opinion bit, I'll just tell you what the main benefits of each god are:
Lawful
Valpurus - Has a valpurium two-handed sword and shield as prizes for two separate prays, championship is prerequisite for best (most impossible) ending
Legifer - Causes a massive explosion centered on you, which is fine since he protects you from the blast (leaving your enemies to take the damage). Also according to the wiki sometimes gives away helmets of piercing perception or scrolls of detect material.
Atavus - Become his champion and you receive an arcanite plate mail, which comes with 18 AV and is thus one of the nicest gifts you can get (it's also very light and thus not hard on the movement speed). Might give away a chest with random stuff in it too, but most of the time does nothing.
Dulcis - Mostly known for her taming effect, which results in everything next to you getting made into your pet. She may also give you a scroll of taming, a Lyre of Charm, a Horn of Bravery, or a Magic Whistle, but I've usually just gotten the song.
Seges - Is generally only useful if you're starving, as then he'll fill your belly to satiated. Piss him off if you want to starve to death.
Sophos - Teleports you to another part of the level. A ring of teleport control won't affect this mode of travel at all (and so Sophos transport is not recommended save perhaps when in dire straits that prevent simply taking off said ring and reading a scroll of teleportation).
Neutral
Silva - Summons pet wolves to do your bidding if above ground, and causes a level-wide earthquake while underground which destroys traps, explodes mines, and causes damage to the walls. Not my favorite goddess by a long shot.
Loricatus - Can harden anything you have equipped in your weapon slot, give you a scroll of repair or repair anything you have equipped that's broken. A very handy god to pray to IMO.
Mellis - Fills empty cans and bottles (up to 5 at a time) with random food/liquid. Sometimes you can get ommel fluids this way. Also sometimes boosts your relationship with other gods (or spreads rumors if pissed). Also very handy for both staving off starvation and putting more healing liquid/antidote liquid/troll blood in your game.
Chaotic
Cleptia - Will bestow haste, invisibility, or ESP on you depending on what you already have (in that order: thus if you have haste, you get invisibility, and if you have that too, ESP). Obvious benefits are obvious (and likely to add to monster difficulty if improperly applied).
Nefas - May grant you the use of one of her mistresses if you have her favor, said mistresses make strong and bloodthirsty pets - good for survival, bad for weapon experience/stat gain.
Scabies - Gives everyone on the level leprosy. Useless against those who don't use the limb system, and awful for the player character given the chances you'll catch the disease yourself (unless I guess you abandon the level for a while while everybody's arms drop off and then go blocking all the non-zombie bite attacks or something). Also can polymorph you into a random creature.
Infuscor - Grants you ESP, telecontrol, or polycontrol in that order depending on which you already have, similarly to Cleptia's gifts. If you have all 3 effects, she will give you 3 teleport scrolls.
Cruentus - Recommends you to Mortifer, gives you a bottle of troll blood or enchants your weapon. Possibly does more than that but I don't recall (as I'm not a very godly player).
Mortifer - As mentioned, giving you a Neerc Se'ulb is the main reason to pray to him (and having two of those is the main reason to pray a second time).