Dimensionality reduction and prediction when all columns have approximately same variance
Concerning the dimensionality reduction
I encourage you to check non-linear dimensionality reduction if PCA does not give satisfying results. It can happen that some low dimensionality manifold hides behind a much higher number of features. The excellent sklearn's guide explains manifold learning in detail.
Concerning the algorithm
Almost any algorithm can manage 15 features with similar variance. It is always the case when you standardize your data before feeding the algorithm with it.
You might want to train any model on a sample of the data and check the results. It can highly reduce the computation time without hurting too much the performance. (there is a saturation of performance with respect to data for a given complexity (features + model's parameters)).
Feature Engineering importance
When performance seems to ceil when changing models, you should consider improving your feature engineering. (products of features, polynomial features, ...)