IPP: The IPP measures the ratio of citations in a year (Y) to scholarly papers published in the three previous years (Y-1, Y-2, Y-3) divided by the number of scholarly papers published in those same years (Y-1, Y-2, Y-3).
SNIP: Source Normalized Impact per Paper measures contextual citation impact by weighting citations based on the total number of citations in a subject field.
SJR: SCImago Journal Rank is a prestige metric based on the idea that not all citations are the same.
Of course, you have the famous journal impact factor (JIF) by Thomson Reuters as published by Journal Citation Reports (JCR). This is based on 2 and 5 year windows. Thus, now we have impact factors on 2, 3 and 5 year windows but based on different databases.
The Eigenfactor is another PageRank-type measure of journal influence.
Scientists normally choose a journal based on factors such as longevity, publisher and reputation in the community rather than impact factor. However, in my experience, in the Indian scientific community, impact factor is given a lot of importance rather than how many times the paper is eventually read/cited. It should be remembered that less than 5% of the total papers that are published are cited more than 10 times (the i-10 index) and only 20% of the papers published in the journal contribute to 80% of the impact factor (Pareto principle).