Agree with propelled. I had not flown since 2011 due to a medical issue but got it back October last year hence needed a part 61 licence. The process was very straight forward. I had to complete forms 61-9TX and 61-9PIC and the cost was 25 bucks. 7-10 days was the processing time last October. Also agree with the advice get the licence and then the ASIC, again this was the way I did it. I did not have to show copies of my logbook.... which to be honest would have last had a flight in 2011 so not a lot of use to them. Needed the ASIC to renew my ratings.
Good luck with it.