PSPP is a free as in freedom replacement for the proprietary program SPSS, and appears very similar to it with a few exceptions. You can use it for One or Two way ANOVA.
Personally I will recommend to use R because of its simplicity in use and a larger community. A number of packages are available, and as a statistical language - it is developed by Statistician for statistician. However, if you are already familiar with the SPSS system then PSPP is a viable alternative.
Prism by GraphPad is also nice. You can get a free 1 month trial to try it out. Very intuitive and straight forward. A good alternative if you prefer not learning the coding environment for R.
Well, you have already many suggestions. For my case I would use R, because of it's range of data analysis, easy to understand, free in online, sensitive in small deviations and so on. However, Minitab is also effective. Regards, Khalil
One more choice is BioVinci, an intuitive, free, and easy-to-use web application that produces high quality scientific figures instantly. Just drag and drop your data.
It also comprises of various statistical functions like PCA, tSNE, ANOVA tests, Linear Regression and some state of the art machine learning methods like Random forest, K-mean clustering...
You could try the example of One-way ANOVA test here: https://vinci.bioturing.com/panel/workset/build/One-way-ANOVA