Hmm I feel like anything I say will be meh, but here goes: (disclaimer: have not experienced all of the below, but am passing on a bit of experience and a LOT of second-hand advice, and extrapolation to an description of a "best-case scenario", so have your handful of salt at the ready).
There's not exactly a single formula for "best build" so play around with what works for you (within budget obviously), but I'll give some basic guidelines for what I've observed.
Bear: is great for survivability (skill is very handy on higher level bears). Additionally, the skill is a passive shield so it's easy to level your riding ability.
Horse: can be good for auto-based build with its dexterity (and good defense). Skill is pretty nice extra skill for some extra damage, but mount skill is kinda secondary to stat boost (generally).
Tiger: good with skills-based builds with the extra energy. Skill is AoE which can make leveling a challenge (makes calling a whole room easy IF you can handle it).
Bunny: IMO best leveling pet; energy + energy regen + instant heals makes it perfect for leveling (especially if you don't level exclusively with combos lol).
Boar: meh, not the greatest, but if you like pulling lots and LOTS of mobs the skill can be nice (and it's a passive skill (as is bunny) so it's easier to level pet ability).
Chicken: No experience with, but I'd imagine it'd be nice for an auto-build and good heals.
Wolf/Dog/(spider): Good dps from skills (if not overlapped).
Dragon/Phoenix: Uhh probably the best if you can afford, but no experience here, so I'll leave that to the professionals.
(edit: you did say gold wasn't an issue...)
I'd first recommend Bear + Bunny (survivability + energy regen for skills and no real need for dex), then Horse + Chicken (attack for autos) for leveling and then Tiger + Wolf/Dog (tiger gives you more energy, wolf/dog helps the dps) for you hit endgame (depending upon build of course, so mix and match).
Recommend building for skills, so as much health as it takes to keep you alive (looking good from what I'd guess, but if you start dying, throw the next few points into vit), as much energy as it takes to kill stuff (varies on skills, so same as vit), and then the rest in strength. (no dex)
Rupture (solid dps): Max,
Pummel (free instant damage, good for animation canceling, but doesn't vary with anything but strength): Max
(Edit: you can have solid builds without pumm, but with the shortest cooldown and animation it's a necessity to use in your rotation even if it's at lvl 1),
Double attack (solid, unavoidable): enough to hurt stuff you're killing (rule of thumb is at least 5 + your level)
Shatter (lowers armor, makes everything much more effective, necessity for group leveling with melee): Max,
Frenzy (attack and damage bonus): All other points
Giant swing is too slow and too often avoided to be a net positive,
Same with sweeping blow (unless you're farming whole rooms at once and can survive it, then by all means use it and warcry (and/or tiger mount skill) and go ham).
Mainhand: Axes are the way to go (look around for a frostiron one (royal is 160 I think) and it's about as good as wyrmbone +shatter skill points). Once you hit 180, mordy str spears, and then gele ax endgame if you're lucky.
Offy: 150, 180, 200 strength axes of whatever element you prefer, then CG ax
Armor: DL set is a good goal, if you can't complete it, fill in with bone stuff, then EDL (if you can't complete, don't break DL), then DG as you can get it,
Neck: 150 sun ammy, stormcaller ammy, elemental damage set, above that look for a guardian necklace or Osan necklace maybe, hunter/poacher ammy, runic ammy, then BT gear
Misc: Offense spider charm or elemental sets (or even just the charm), BT gear
Braces: should be good for a bit, then look around for some nice offense Hrung braces, a good necro recast brace (pummel or double attack recommended as rupture runs into itself if you cool it down too quick), then you're looking at prot/gele braces, hellforged/apostate
Rings: skill rings should be a big focus, alchem/jagged ones are ok, but try to get some silverweb ones, and then Gele ones, then BT ones.
Haste: not all bad, worth it enough to have ring/offhand at endgame (but reaper is overrated for it's price
Other: On mount/pet, if you have what you know you're gonna use at endgame, max out that sucker at the top level, but if you think you're gonna change for endgame, I'd recommend getting max tier on lowest level (ex brown bear rather than white) cause you're still getting most of the benefit, without as much spent and not as much wasted if you do get a different one. Beyond that, I'd recommend getting your mount to a speed you're comfortable with (80%ish for me) then focusing on leveling up pet to max before going further with pet.
And above all, have fun! Play around with it, see what playstyle you like, because as soon as you stop having fun (breaking it down a bit too much into 1s and 0s), is when motivation goes away.Did'nt mean for that to be that long, I really don't know what I'm talking about that much