There is plenty on this with a google search. This should get you started: http://www.graphpad.com/www/book/choose.htm
Yes there are a number of decisions you need to make before analysis to determine which method you will use. From your explanation, it sounds like your groups are independent (or un-paired as they describe in that webpage). Also, the word "Gaussian distribution" is another word for "Normally distributed".
Once you have an idea of the test you want to do, just google "test name, with assumption spss tutorial/example" etc and you will easily be able to find a step by step tutorial and interpretation guide for spss without dramas.
It sounds like you are on the right track anyway with your independent samples t-tests. The p-value of your tests which you use to determine the significance are influenced by sample size, and standard deviation. So, if you wanted to get robust p-values, you will need to increase sample size, and/or decrease the SD (perhaps by using reliable measures). That said, if there truly is no difference between the groups then no amount of working the stats will turn a non-significant result into a significant result (and you don't want to mask the true relationship anyway). If you have accounted for the assumptions of the t-test, then you will just have to accept that some of the variables are not different and will need to explain this somehow (might be a problem with methodology or perhaps there actually is no difference in the population).
Hope this helps