When intending to (or potentially might) use an amp sim, Melodyne (Melodyne can fall apart when trying to process a signal with harmonics already existing), or external send for re-amping it is best to actually record a clean guitar signal with the best S/N ratio you can get initially. You may be able to achieve this from your interface alone (would need to test), as you can record a track and then normalize it before then doing any of the above.
The advantages of an active DI box are to boost the signal for recording where the interface doesn't cut it as well as allowing for very low monitoring when tracking by also splitting the output giving you the flexibility of using a real amp to monitor while tracking that signal (which you can also record with a microphone if desired). To achieve these best, mute both the clean/microphone tracks while recording and simply listen to the amp while tracking.
The "purpose" of a DI box (for signal boosting) can also be achieved via any powered external pedal/processor which can boost the clean signal (which you may already have), but the routing of a DI box (two signals, one clean for recording, one colored for monitoring) may not be readily achievable.
As far as tone... the purpose of recording a clean signal is you can use EQs both pre/post processing (via amp sim or external re-amping) to color that tone to your heart's content. It is often easier to take away than add, so I always shoot for the best clean S/N ratio of the full signal on the recording and let the amp sim do the rest post-production. The biggest advantage of an amp-sim or reamping is you can change your mind down the road without having to re-record anything. Amp sims are the easiest to work with, and a post-EQ LPF in the 4K-7K range seems to have the biggest bang-for-the-buck to harness harmonics created which an amp itself would not.
I just wanted to throw this out, since an active DI box is intended to boost the clean signal, not "color the tone," per se. As long as you get a good S/N ratio, you also have the possibility of normalizing a recorded track and gating the normalized track to remove the boosted noise in most cases. Active DI boxes do have advantages in signal boosting and monitoring options while tracking.
With all that said, I looked into an active DI box in the past, but realized 1) I already had a processor to do what I wanted, and 2) didn't need the processor since my interface alone can achieve proper signal gain with low enough latency to monitor via amps sims once I streamlined my tracking process.