Evolution precisely has two elements:
Darwin himself did not know that these changes can result from random genetic mutations, he knew nothing about genes, much less DNA. He only knew that offspring are sometimes different from their parents.
Darwin deduced "natural" selection based on his knowledge of human selection of domestic animals. Just as a farmer selects the best looking pig in a litter to breed, so nature "selects" those offspring best suited to survive.
That's it. That's precisely what the word "evolution" means.
Of course, from that many other ideas can be deduced (or debated), but the word "evolution" itself is a very simple and basic scientific theory which can be and has been often studied, observed, and never proved false.
As for the long, long-term emergence of, in your words, "viable new types of creatures", the word "type" is not a scientific category, and might be construed to mean almost anything.
Examples in nature of related species just on the cusp -- so different they can interbreed, but the offspring are sterile -- include horses and mules, along with according to some researchers, Neanderthals and Cro-Magnons.
But fossil records, and DNA analysis, show evolutionary time separating horses from mules, or Neanderthals from Cro-Magnon in the million-year plus range.
So clearly, in nature, such changes do not normally happen rapidly.
But nothing known to science prevents many small, incremental evolutionary changes from adding up, over many millions of years, to the development of new breeds, species, genera, families, orders, etc.
So, whether any of these scientific categories (i.e., breed, species, genera, etc.) corresponds to the biblical "kind" or your word "type" is really only a matter of interest, I'd suppose, within ID/Creationist circles.
Ooooooops. This example should say "horses and donkeys" which when mated produce sterile mules, of course.
1. Descent with modification -- meaning offspring are not just carbon copies of their parents, but sometimes contain changes.
2. Natural selection: meaning that those offspring with changes which better adapt them, helping them to survive and reproduce, can pass these changes on to their offspring.
Everybody accepts the idea of speciation. Speciation is not evolution. There is no evidence that the progressive branching of life that evolution espouses could ever occur.
There is no argument that all canines very well could have started with a single variety of dog or all felines could have started with a single variety of cat, but there is no evidence dogs could ever become cats or anything else, through any number of intermediaries.
It's hard to phrase what "type" means in a biological classification sense as that classification is certainly prone to errors as is any other man devised system. My feeling is that type may be generally defined as what is classified as a genus, but may possibly extend beyond that in some instances.
The so called fossil record is meaningless. It's nothing more than starting with a pre-concluded assertion and fitting the data to fit that conclusion. There have so many proven misrepresentations, hoaxes and inconsistencies with the fossil record regarding evolution that I laugh whenever anybody offers it as evidence of evolution. I know you don't agree, but whatever.