You don't have to learn 'frequentist' or Bayesian statistics in any particular order. You should first learn whatever you need to understand the findings in your field, and then you should understand the mathematical (computation) and philosophical (interpretation) relationships between the techniques. There is no teacher like real data, so that is always the first concern.
There's no particular reason you couldn't learn them at the same time. It's helpful to know the gist of calculus for Bayes, which is presumably where its reputation for being "harder" comes from, but I wouldn't call it necessary now that we have much better software than just a few years ago. If you are new to statistics and want to play around with both the frequentist and Bayesian framework, I can recommend the new JASP software. If you like R, the BayesFactor package is solid.
If you want to start from frequentism, I would suggest knowing the following:
- The full and exact interpretation for all of the following items.
- The relationship between p-values, confidence intervals, sample sizes, power and error rates.
- The relationship between Z-tests, t-tests, analysis of variance and linear regression.
- The relationship between linear regression and nonlinear regression, as well as parametric versus nonparametric tests.
- The relationship between dummy variables, contrasts and effects coding.
- The full and exact interpretation for all of the preceding items.
That sounds like a lot, but these things are all connected in fundamental ways. Every inference boils down to the same essential thing: we want to make correct predictions about unobserved data, based on a model of observed data, by comparing two or more models. We do this by computing our confidence, for some definition of "confidence," in two or more models and taking the ratio. At its most basic, that's all.
A lot of the controversy is really just about formalizing "confidence," and while it's an important discussion that I'm glad we're having, it's also not something you need to be aware of right now. In the frequentist framework, special steps are taken to create an implicit null model to put in the denominator, whereas in the Bayesian framework, both models are stated explicitly, but the actual output and interpretations for both frameworks involve a substantial degree of subjectivity. For frequentism, it's in the construction of maximum likelihood and choice of error rate, and for Bayesians, it's in the prior. Everyone should learn both, in my view.