Always focus on PvE first, especially if you're F2P. Only way to can try to compete is to maximize PvE dmg and thus silver. If you fall behind you will continue to fall further and further behind.
Rukia + Renji would be my first two along with Rang you have a great PvE team. Then work towards kisuke asap, then Ikkaku. The PvP partners like momo/harribel/yoru are for after the PvE characters. Winning at PvP gets you far less than winning at PvE since most of the time a good PvE team will still do quite well in PvP and you'll have a lot more BP in PvP from all the extra reiatsu. See if it matters what partners they have if you go first and kill half of them before they even attack.