As far as I'm aware you need a PC in order to root, and you need root to install ROMs so no it's not possible.
There is no such thing as a best ROM. This is because we all have different wants and needs as far as ROMs/kernels are involved. Have a look at the development threads and see which ROM suits you best. 'Best ROM' threads usually start arguments, so therefore they're not allowed and are usually deleted by mods