Nice to see Roger Hicks on APUG. Welcome back!
To the OP: The Kentmere papers are now made by Ilford, as you may know, but if the new Kentmere paper is anything like the old one, its contrast will be different from the Ilford one. The multigrade paper also didn't work with the Grade 4.5 and 5 filters, when doing split grade printing, which I always though was strange.
Roger's recommendation regarding the Ilford Art 300 is interesting. I find its texture to be very difficult to deal with when there is a lot of black in the print, particularly if the black consists of even tone. The paper texture gives strange reflections, making it difficult to actually see shadow detail. For some things I personally find it incredibly beautiful, usually portraits and other things with fairly close focusing. (that's my personal view anyway).
When it comes to photo papers, I always recommend, as a general practice, to have one main paper and paper developer. You can have others, but make one your main paper/developer. What you'll come to realize is that the paper and developer is capable of a certain tonal range, and a certain tonality. Now you need to learn how to make negatives that best fit that paper and developer combination. Once you have mastered this, your darkroom efforts will be a lot less demanding because printing becomes easier, but most of all you will waste a lot less paper, which I find important in this day and age of high cost, environmental concern, and as a bonus your results usually improve too.
In the end I doubt it matters much whether you choose Ilford or Kentmere, just as long as you consistently use the same. This whole process becomes easier the fewer films and developers you use too. I understand the lure of using many different ones, but same as with paper I recommend using one main film/developer combination, and experiment with the others on the side.
Have fun!