The product page lists it as Ash which, TTBOMK, is likely American Ash aka White Ash. FTR it most definitely is not to be confused with Swamp Ash. The Ash supplied in the PBG kits tend to run quite heavy. However a lot of them have reasonable grain patterns. Hopefully you got something that's not made up of too many pieces, and the pieces match reasonably well.
Ash is a very open pored timber and requires grain filling if you wish to have smooth finish (satin or gloss). There are numerous products available for grain filling nowadays, so pick your poison! If you want to accentuate the grain, you can use a contrasting coloured grain filler before staining.
This is my TLA-1 (ash tele) that I'm currently refinishing, and I used Ebony Timbermate grain filler followed by alcohol based dye then polyurethane:
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