Your group composition is great for PvE:
- Paladin is a very easy tank to box with, and possibly the strongest on multi-mob pulls.
- Priest has amazing group heal ability.
- Shamans have great burst and everyone operates off of mana, which helps.
- You could BG PvP with this setup fairly easily, Pally heals, Priest goes shadow and everyone is ranged attacks.

As a paladin, you want to click:
- Avenger Strike (to pull), Holy Shield (a ton), Consecrate (aoe and most pulls), and the occasional other move (Hammer of Righteousness, Hand of Freedom, a buff).

On the shammies, you'll want:
- Lightning Bolt, Chain Lighting and eventually Flame Shock + Lava Burst. Plus your totems.
- You can combine a lot of these abilities to be on the same keypress. For example: Q = Holy Shield, Lighting Bolt, W = Holy Shield, Chain Lightning.

Buff up on a Key:
- I have my totem farm keybound to Backspace. Pick three Fire, Water, Air and Earth totems which you'll use on almost all pulls.
---- Shm A: F-Totem of Wrath; W-Cleansing Totem; A-Grounding Totem; E-Strength of Earth Totem
---- Shm B: E-Tremor Totem; W-Mana Spring Totem; A-Grounding Totem; F-Magma Totem
---- Shm C: A-Totem of Wrath; W- Healing Stream Totem; E-Stoneskin Totem; F-Magma Totem
---- Priest /castsequence [target=paladinname] reset=5 Inner Fire, Fear Ward,,,,,,, Prayer of Fortitude, Prayer of Spirit
(With the priest macro, several additional presses will group buff the party, but it will reset to the initial buffs if the macro is not clicked at all for 5 seconds)
---- Paladin /castsequence reset=5 !Concentration Aura, Seal of Vengeance,,,,,,
- In addition to a totem farm, you may occasionally want 3x Magma Totem, 3x Earthbind Totem (staggered for the root), 3x Fire Nova (staggered for the stun), 3x Grounding (for vs ranged casters). It's nice to be able to dump them on a keystroke.
Something like:
/castsequence reset=5 Earthbind Totem,,
/castsequence reset=5 ,Earthbind Totem,
/castsequence reset=5 ,,Earthbind Totem

You could probably combine a decent AoE macro... Consecrate, Magma Totems x2 (and Totem of Wrath x1), and maybe Earthbind for the root. Priest could Holy Nova or Prayer of Healing on this keypress.

The Pally will want an initial pull macro, without the others doing DPS.

I'd probably have a few keybinds for AoE heals, and possibly work Renew on the tank, into the automatic damage/Holy Shield.
Priest could easily have: /assist Paladin.... /castsequence [target=targettarget] ,,Renew,,
Which would have the priest cast renew on whoever the target of the paladins target is, once out of every 5 clicks.

One thing you could try... go into keybinds and change one of the priests keys to a side button on your mouse.
Put Flash Heal on this key and make a macro.... /cast [target=mouseover, help] Flash Heal. You can do the same with other heals too.
Now you can have the priest quickly heal whoever needs it, by mousing over them and not even needing to move the mouse to click something.

Everyone has their own system, but combining keystrokes will probably help you out a lot.
Tinker around with your set up often, incorporate anything which looks neat. You can always improve upon what you have.
If you find something that works particularly well, post it too; others might benefit from what you've found.
I'm not familiar with HotKeyNet, so cannot help with your script at all.