I have heard that koh-i-noor white colouring pencils are very good, however - I have not tried this brand myself; did you receive a white colouring pencil in your koh-i-noor set, as you stated that you commenced drawing with this specific brand?
I agree, I have heard a vast amount regarding lead breakage of Prismacolor pencils, which is a shame; as they have a lot of potential. However, I suppose it is ultimately down to whether you prefer wax based or oil based pencils.
Unfortunately, lead breakage is the identical reason I discontinued using Derwent Graphite Pencils after about 2012, as the leads fractured and broke easily; when attempting to sharpen the pencil, irrespective of the quality of the pencil sharpener or whether a different means was utilised, it would always cause the pencils to split the wood of the entire pencil itself, rendering them useless. Hence, I now use Faber Castell Graphite pencils, which are better and more durable, in my opinion.
I recommend you try the Daler Rowney Georgian Water Mixable Oil paints; they are an excellent alternative to oil paints if the latter is not viable or you dislike the smell of turpentine/white spirit that is used alongside traditional oil paints.
http://www.daler-rowney.com/georgian-wamoWhilst these paints can be used with water, it does remove some of the vibrant pigment from the paint; thus it is recommended that linseed oil or water mixable oil paint thinner is used, which can bought from Hobbycraft, art and craft stores and online. Thus, this means that the intense pigment from the paints is retained whilst mixing other colours.
I actually use these paints myself and am pleased with the paints.
Furthermore, I use Winsor and Newton Cotman Watercolor sets (half pan), which I find to be excellent, though the 45 half pan set can be purchased on Ebay, for a lower price than that of Amazon. However, I recommend you try the pocket set first (this is what I did), to see if you like the watercolour paints themselves; furthermore, although there is no black pigment in the pocket set, this can be easily achieved by mixing 'burnt umber' and 'ultramarine blue'.
https://www.amazon.co.uk/Winsor-Newton-Cotman-Colour-Paints-x/dp/B00004THXI/ref=sr_1_9?ie=UTF8&qid=1490970300&sr=8-9&keywords=watercolour+brushWhite Night Watercolour paints are apparently excellent too:
https://www.amazon.co.uk/White-Night-Watercolour-Whole-Plastic/dp/B006FHNDH4/ref=sr_1_20?ie=UTF8&qid=1491652543&sr=8-20&keywords=watercolour+paintsRegarding acrylic paints, I recommend that you try the Daler Rowney Graduate Acrylic Paints 120ml, which are often on sale at Hobbycraft for £1.50 each; which last quite a while! I like to collect them over time, purchasing a few at a time so that I eventually have a spectrum of colours to use in my work. However, I have also used Daler Rowney System 3 Acrylic paints, as well as Winsor and Newton Acrylic paints; which are also excellent. Moreover, I have heard that 'Sennelier' is a good brand for acrylics, as is 'Pebeo', although I have never utilised these specific brands myself.
I hope this helps!