The Underground platforms are a fair walk from the EMR platforms at St Pancras, but in fairness so are pretty much all onwards transport links other than the Thameslink platforms.
Step-free access (via lifts) is available at Kings Cross St Pancras, Victoria and London Bridge so either the Victoria or Northern lines are both plausible options.
My personal preference would be to go for the Northern line to London Bridge as both te Northern line and Thameslink trains tend to be quieter in my experience, and the latter are more spacious and have better luggage racks.
That said, you might prefer Victoria as it's a slightly longer walk between the Underground and National Rail platforms at London Bridge than at Victoria. Also, the NR platforms at London Bridge are elevated above street level and there's only one lift per platform so there can be a queue to use it at times - at Victoria, the NR platforms are at street level.
If you preferred to take the bus, the 390 runs to Victoria every few minutes from the south side of the Euston Road. The 17 bus runs to London Bridge every 10-12 mins from Pentonville Road on the east side of Kings Cross. You avoid the lifts down to the Underground platforms and back up, but it's obviously slightly slower overall. This would be free with your ENCTS pass of course.
Otherwise there is the most convenient but expensive option of hailing a black cab from the rank outside the Thameslink platforms at St Pancras. Based on TfL's estimates on their website, it would cost around £18-25 depending on traffic. A taxi ordered via Uber etc. would tend to be cheaper but I'm not sure whether they can pick you up there.
