I am constructing an inflation factor that includes the gdp deflator, the PPI for finished goods, and a spot commodity index.
Do I uses seasonally or nonseasonally adjusted historical series?
It depends on the intended end-use of your model, but generally-speaking, if you were solely trying to measure and forecast inflation levels or the GDP deflator over the course of a year (including the use of, say, the GDP deflator percentage change in March, as a factor that somehow goes into your April forecast), you would need to consider seasonal adjustment factors due to the impact weather and other related events have on purchasing patterns, commercial and industrial activity levels, the influence of taxes on PPI, etc. That being said, it might be a lot easier to use non-seasonally-adjusted data, which could be okay if you're only using it as a factor to forecast and analyze year-on-year (YoY) changes (as part of a time series, for instance). While seasonally-adjusted data is great in theory, data limitations and BLS revisions to the seasonal adjustment factors (which occurs every January) may limit the practicality of this approach. For more detail, as you will likely want to get a strong understanding of the data series you are going to use if you want it to be of any value to a model, see https://www.bls.gov/cpi/seasonal-adjustment/intervention-analysis-seasonal-adjustment-2018.pdf. Here, the BLS explains in detail why and how it performs what it calls 'Intervention Analysis in Seasonal Adjustment,' which is something you will want to understand. Also, note the BLS recalculates its seasonal adjustment factors every January for the preceding year's data and notes that this routine annual calculation "may result in revisions to seasonally adjusted indexes for the previous 5 years." This could just add another nuance to your modeling and introduce potential errors, depending on the regularity of your data collection, etc. Note also that BLS will make available recalculated seasonally adjusted indexes, as well as recalculated seasonal adjustment factors, for the period January 2014 through December 2018, on Monday, February 11, 2019 (updated data will be released here), so you might want to look out for that updated data series if you do use seasonally adjusted figures.
Hope this helps. In short, some things are great in theory but aren't all that practical in reality. Then take into account all the assumptions and other potential sources of error in an econometric model and it may seem more effective to use the unadjusted prices. It is ultimately your choice and depends on the amount of time and resources you will devote to the project, but generally, if you are attempting to build a robust model, you might want to find a way to avoid the revised, seasonally-adjusted data.