Do not set the AVR to Bi-amp unless you have Bi-wire capable speakers and use 2 sets of speaker cables per speaker - one for tweeters and one for woofer - AND no jumpers between the bi-wire speaker terminals. Otherwise, you will damage the AVR and possibly your speakers. My advice is to ignore this option.
Also, if I remember correctly, the Bi-amp option uses the power sections of the two rears in the 7.1 setup, so you are limited to 5.1 if you use Bi-amp to your front speakers. It sounds like you plan to do 7.1, so this is yet another reason to ignore the Bi-amp option.
The Onkyo AVR's have excellent power supplies and should drive your 4 ohm load speakers with no problem, so just leave the BTL/Bi-amp settings at the factory presets.
The purpose of 'pure' and 'direct' modes is to pass analog (un-digitized and unprocessed) sound to two full range front speakers, especially when using a turntable through the phono inputs. The way this (and most every) AVR is designed, it has to convert the analog signal to digital to implement the LFE (subwoofer) channel and that is usually not desireable when using analog sources.
Another side-effect of using 'pure' and 'direct' modes is that the Audyssey room-correction is bypassed. Once you run Audyssey, I think you will prefer the sound using the 'Stereo' mode so that the LFE (subwoofer) channel and the Audyssey room-correction are engaged. Possible exceptions (in addition to using a turntable as a source) are acoustic or chamber music that is recorded well enough to benefit from staying in the analog domain in the AVR. Even then, the D/A converters and the analog section in your disc player (and very good analog interconnects) will have to be better than the Onkyo's or there will be no benefit above using the 'Stereo' mode fed by a good coaxial digital cable from your CDP.
As you become more familiar with the Onkyo, I think you will find that it is designed very intelligently for the purpose it is intended for - to be a full-featured all-in-one component at a relatively low price point. If you desire more audiophile features and cutting-edge sonics, then consider hi-end HT separates such as Anthem, B&K, Marantz, etc.