It sort of depends on what you want out of a squadmate. I will tell you my preferences for those two specifically with a Vanguard.
Liara
Singularity: I invest here first to get at least 2 ranks for Recharge. Then it is leveled for Duration, Lift Damage, Expand. The early duration helps setting up combos before you get all of her recharge bonuses. If you are starting leveled up or respec'ing you can go Radius instead, it is no big deal. For the most part this
Warp: This is an important all around power on Liara because it primes any target with any protections in the game, it has a Detonate evolution which is a biotic combo multiplier, and it has the Expose evolution which is a damage taken debuff. Even though Singularity is very powerful, I tend to say Warp is her best all around power since it can do a bit of everything and is best for combos. I also wouldn't be surprised if Incendiary Ammo (the power) has a similar glitched DOT interaction with Warp in SP (it inherits Warp's multipliers), although I don't think it has been formally tested.
Stasis: This is really a take it or leave it power to me. The reason I don't care for it in SP is that the vast majority of enemies are health only and Singularity will CC them. So then you are left with the odd shielded target that you can CC, but I don't find there is all that much utility to be had there. Vanguard can make its own CC via Charge for staggers and detonations, and you can set up better biotic explosions on shielded targets with Warp. Since you can't use Stasis on armored targets, the niche is pretty small. I only find it somewhat helpful vs Phantoms in SP, but they aren't common enough that it is a big priority, nor are they typically a huge problem for a Vanguard anyway (just don't charge them when they have just slashed something).
Warp Ammo: Another one that you don't necessarily need. Especially as a Vanguard since you have the best ammo power already. You can dump points in this after all the others are maxed, or start dumping points after Singularity, Warp and Passive are completed.
Pure Biotic: Basically you want Recharge, Duration and Force, Squad Bonus here. More shields don't do much for her, and her weapon bonus isn't useful either. Singularity benefits from the Squad Bonus and will be on a very fast cooldown by the time you get to the last rank anyway.
EDI
Incinerate: Assuming a Vanguard and Liara as the second squadmate, I would probably invest here after I already spec'd Overload to at least Rank 4. Once you do I would go Damage, Recharge, Armor Damage. The base radius took a step back from ME2 and I don't find that the 1.5m bonus hits multiple targets very often. Recharge just because you will end up using it for combo priming more than slow DOT most likely, and Armor because you aren't going to be chilling anything.
Overload: I almost always level it by Chain, Neural Shock, Shield Damage because that should give you enough damage to shield strip a Level 60 Phantom while also giving a little extra CC via the first chain. Neural Shock is mostly for the drastic increase in organic damage rather than its incapacitate function. Alternatively if you don't find the single chain to help you much, go Damage at Rank 4 for the highest damage you can get. I haven't bothered to run the math for synthetic damage relative to Hunters and Pyros, but they are so limited mission wise I tend to not care about that.
Decoy: I don't spec this. So basically EDI sits around with a zillion points by the end of the game for me. But if I were to spec it, then the best would likely be Duration, Shock, Exploding.
Defense Matrix: I don't tend to spec this either because she doesn't necessarily need the power damage bonus or the extra DR. If I did it would be Durability, Power Synergy, Power Recharge.
Unshackled AI: Power Damage, Tech Damage, Squad Bonus. She is there for Power Damage, and most squadmates don't do enough weapon damage to make generic weapon damage bonuses worthwhile (exceptions are Ash, Garrus, and Zaeed because of a couple other evolutions).