The show is fairly explicit about Walter White being an extremely gifted chemist, and only being a teacher rather than a multi millionaire because he'd left the company making money from his innovations because he was in a sulk that his co-founder was dating his ex, and he just assumed that he was going to be able to make a second multi million dollar company on his own and that his friends hadn't contributed at all.

The meth was better quality not just because he used the right equipment, but also because he put what other people considered an unreasonable amount of effort into avoiding trace contamination, and intuitively knew which unwanted reactions he needed to worry about and take measures to avoid. In a later episode, Jesse has to demonstrate how to make comparable quality meth to some professional chemists who have been failing to do so, and the only thing he can find that they've been doing wrong is not keeping things clean enough. After meticulously cleaning things that were already deemed clean, he gets something close to Walt's results.