Start with linear kernel and see if your data is linearly seperable or not. Performing that is simpler than looking for early indications.
Linear kernels are suggested when the number of features is larger than the number of observations in the dataset (otherwise RBF will be a better choice).
However, once you conclude that you have non-linear data, you ...
The fact is that in Unsupervised algorithms, you never know. That is their main bottleneck. Unsupervised algorithms (Clustering, Dimensionality Reductions, etc.) are based on assumptions. When an assumption is made, then it will be translated into a math algorithm and applied.
Choosing the right thing, as you said, is possible only if you know how is the ...
It can be hard to choose - because it's hard to visualize. However, you probably have a specific goal right? Maximizing some kind of score.
Why don't you try a Grid Search applied to your dimensionality reduction decision? See this.
I'm interested in reading other, more theoretical answers to this question, though.
In simple terms: Linearly separable = a linear classifier could do the job. You could fit one straight line to correctly classify your data.
Technically, any problem can be broken down to a multitude of small linear decision surfaces; i.e. you approximate a non-linear function with a high number of small linear boundaries. That's what Neural Networks are ...