This is at the same time a fairly simple subject and yet complex due to the number of variables that can be brought into the equation.
Disclaimer: I'm not technically proficient enough to point you in the right way but that hasn't stopped me before so I'll give you my 2 cents)
At the basic level we should understand that with regard to resolution raster imagery will always be of lesser quality than vector.
Bitmaps vs vector lines and shapes... it might help to consider this in terms of loss of data.
With bitmaps/raster imagery we are dealing with a finite canvas.
This is opposed to vector imagery that stores calculations that recreate those lines and shapes at any scale.
Some techniques are used to maximize raster imagery but we can't really get more out of raster than what we initially put in.
So we have to have that starting point, which for all intents and purposes seems to be the underlying question you are asking here.
With raster imagery there are two basic approaches to maintaining what is already there; this gets into the realm of codecs... encoding and decoding... lossy and lossless. Do we want to maintain what we currently have or can we lose some of the data without adversley effecting what is seen there.
Skipping ahead a bit... perhaps the most important thing to do would be to frame your question in light of the target device.
This may have more to do with your hardware, your monitor for instance, than anything else.
An herein lies a question for you. It seems to me that your concern is based on workflow at present and not the final product.
Is it just your eyes? Well, maybe.
If you are working with raster imagery you will always have pixelization as that is the nature of bitmapping.
So, what to do?
Well, one thing you could do is stop zooming in so closely on those pixels! ;)
Zoom out instead.
Then notice that you see less pixelization.
It's magic I tell ya!
Perhaps more importantly than all this is the final product that you want to deliver/present.
But that doesn't seem to be the primary issue at hand here although after your workflow is hammered out it surely will be.
Aside: One thing we can do in OT that can't easily be done is many other programs is to convert from raster to vector *after* we've accomplished what we intend to do at our working resolution.
While I don't always do this I often like to draw black and white linework in raster and then convert that linework to vector to achieve and lock in 'infinite' resolution.**
There is nothing... outside of our preferred workflow... that prevents us from moving back and between raster and vector formats as often as we like other than that each time we move to raster we risk losing image fidelity/accuracy in the process as the math takes over.
But, the bottom line is that if we want to avoid pixelation we need to move away from raster to vector. Then the question of resolution becomes largely moot.
**@JJParks mentioned this and it follows pretty standard industry workflow. Whether the initial imagery is scanned in first or drawn in raster the final linework/inking is more often than not done in vector in order to achieve the smoothness of vector's infinitely resolution. OT gives us an advantage in how easy it is to move from raster to vector (and back and forth again repeatedly if we so choose).
Added: One thing we should probably look at is why your are experiencing issues with vector drawing. When you state that 'vectors run too slowly on my maching' that may be well worth looking into.
My number one rule of thumb when operating with vectors would be to save often to free up resources but other than that we'd probably need to know more about your computer's setup.