You've got to have some specific power combo you want to make multiclassing worth it in SF, it's certainly not the answer to everything.
To make power armor work - powered armor gives you a set strength. You need some strength to gain proficiency but this is higher. From level 10 up they give you reach. A level 2 upgrade available only to powered armor is the Automated loader. A level 14 upgrade available only to powered armor is the Titan shield. That's all that powered armor gets that heavy armor doesn't. Somehow you need to use those to make it worthwhile.
Some free effective strength lets you be at least part-time melee while spending stat points elsewhere. The automated loader might be useful with a weapon which goes thru ammo fast, a flamethrower or a sniper rifle, or an automatic weapon. A soldier who goes with the bombard fighting style can make the last of those worthwhile perhaps, and it fits with the idea of the automated loader well.
In summary? I'd make the character a bombard soldier, go around packing a machine gun or similar on my powered armor and look for opportunities to catch many enemies in the cone of fire an automatic weapon allows.
First thing you want to do is read all of the power armor section so you aren't building something that doesn't work for your build.
Blitz would get you an improved bonus to initiative and a +10 to land based speed, at third level weapon specialization and a gear boost.
Now having 10ft out of combat is nice but it's not going to help in power armor because power armor has it's own speed.
Speed:
Rather than using your normal speed, the powered armor has a
maximum land speed of its own. In some cases, powered armor
has additional movement types as well.
If you aren't going to be using melee a lot I would pick another fighting style.
Question: What is your characters backstory? What's the concept? If you define that it might help us to narrow the search down.
As avr and JetSetRadio mention, you need to make sure you're not working against your build. You need some (13) Strength, but don't want so much that the armor isn't a boost (my Armor Storm soldier has 21 Strength and the Battle Harness would be a debuff). Your speed doesn't matter once you get the armor at level 5, because the armor has its own speed and your personal bonuses don't apply.
One thing you may want to do is... actually just wait. The Armory book coming in July is going to have a pile of new power armors. I'm planning a Nuar Technomancer who is looking forward to the spellcaster-oriented power armor suits rumored in the Armory. So maybe inspiration will strike you for a build in the next book.
I actually really like the Bombard Soldier/Mechanic combo. Between the soldier's free grenade and the mechanic's Overload Weapon to use discarded enemy weapons as grenades, you get a lot of boom to go around (though the overall lackluster nature of grenades is still an issue). It is unfortunate that Heavy Fire doesn't stack with Overcharge, though. You have to choose between +damage dice or +Strength damage. I would go Bombard Soldier 3 and then switch to Mechanic if I went that route because Overcharge scales better as you invest more Tricks into it.
Be for regular or powered armors, here is something blatanly missing:
Mobile Army (Ex) 13th Level
D You become a master of all weapons associated with your
armor. You deal 1d6 additional damage with any attack from a
weapon that is part of your armor, including unarmed attacks
using the hammer fist ability and weapons that have been
attached to your armor as an armor upgrade. The additional
damage is of the same type as the weapon’s normal type.
Also, while wearing heavy or powered armor, you gain a +2
bonus to your KAC against combat maneuvers.
Emphasis mine... I've checked and re-checked the rules, but that upgrade is missing :P I don't think it's the quick-release sheath, because it looks like a simple storage option, not about attaching a weapon. True, ranged weapons can be attached to powered armors, but nothing has been written for melee weapons.
One more thing that would be useful is a free upgrade, or upgrade that takes little to no slot, that increases Strength or even Dexterity.
Be for regular or powered armors, here is something blatanly missing:
Mobile Army (Ex) 13th Level
D You become a master of all weapons associated with your
armor. You deal 1d6 additional damage with any attack from a
weapon that is part of your armor, including unarmed attacks
using the hammer fist ability and weapons that have been
attached to your armor as an armor upgrade. The additional
damage is of the same type as the weapon’s normal type.
Also, while wearing heavy or powered armor, you gain a +2
bonus to your KAC against combat maneuvers.Emphasis mine... I've checked and re-checked the rules, but that upgrade is missing :P I don't think it's the quick-release sheath, because it looks like a simple storage option, not about attaching a weapon. True, ranged weapons can be attached to powered armors, but nothing has been written for melee weapons.
One more thing that would be useful is a free upgrade, or upgrade that takes little to no slot, that increases Strength or even Dexterity.
Yes, I suspect that there was originally a rule for adding weapons to power armor as an upgrade, but they removed it in favor of just giving weapon slots to each power armor. I was bummed, because my Armor Storm soldier would have loved to build weapons into his heavy armor with his 5th level ability, Enhanced Tank.
My guess is that we will see armor upgrades to add strength to power armor, because there should be an option where max strength characters don't take a nerf to wear the best armor. The only trick is how that will interact with Armor Storm soldiers installing it into heavy armor... does the soldier then get the boosted strength, or will it be written so that it specifically only works for power armor (at which point the value of that aspect of Enhanced Tank starts to seem questionable).
I will be curious to revisit this in a couple months once the armory is out which sounds like it should flesh out power armor to be more generally usable and even having a spell caster version for use.