When adding figure into "Cost of Land" for rental asset, which figure am I using from the tax bill? Land appraised value? Or Assessed value? From current or purchased yr?

When you acquired a rental home, the cost basis is divided into land (not depreciable) and improvements (the house itself) which are depreciable over 27.5 years.

The most common way to apportion the cost basis between these two parts is to prorate the cost basis using the respective values of land and improvements in the Appraisal district  latest appraisal at the time of acquisition. You then keep these same values during the useful life of the home.

tax bills do not necessarily reflect the actual FMV of land and the building at the time of acquisition.  you'll know this if the total of the two don't add up to your tax basis,   for example, land may be valued at only 10% of assessed FMV (not appraised value) so if land had an assessed value of 70K only $7K may show up on the tax bill.