Maybe 70 days to be safe (assuming you properly post and document the 5 day etc)
about $250 total for the filing fee and writ of possession
If you don't need to file yet, go to JP court and watch "justice" in action. It helps to see where others fail/screw up/etc so you can try to skip those steps in the future
As an aside, if at all possible, I like to evict for multiple reasons - If you just post a pay or quit and they show up at court with the money, late fee, etc, then the JP won't evict them, and likely have a pissed off vindictive tenant who you get to stress about next month.
Instead, you post the pay or quit and a cure or quit for that dog you noticed a few months back, the excess trash in the yard, whatever violates your lease. You're much more likely to be successful when they can't prove they fixed whatever violation you found. If I start the process, I finish it - I don't want to wait months to see what some vindictive SOB has done to my house.
In Texas, you don't even have to be an attorney to be a JP - these guys and gals are a special breed, and expect to be treated as such. That said, they do not always follow laws, statutes, rules or common sense. If you have a tenant who can really pull some heart strings, expect to wait longer, even if you are totally in the right and show up with all your shit together.