how long it should take from me to build tier 1 till tier 3 back links for my site without spamming google for indexing my links
SEO is a LONG process! You'd better build backlinks for 6 months for example than trying to speed up the process by building backlinks for 1 month! Let's say you create 5 web2.0 sites for your 1st week! Then wait a few days for Google to index them NATURALLY! Then, let's start tier backlinking, you should work continuesly and build backlinks EVERY day (no matter if this is done automatically, but it's much better if you do it EVERY day for about 15 minutes for example than working 10 hours for ONLY one day!). Then just continue doing this and you will see success in the next let's say 2-3 months (this depends on the keywords!)
You can be much more aggressive with link building on your tier 2 and 3 links - adopting a "throw as much as you can and see what sticks" is a pretty safe plan of action PROVIDING you stay away from this method on your top tier. WebDev