First of all, congratulations on your first directing gig!  All I can say is: Get yourself a seasoned stage manager.  They are worth their weight in gold and will be able to help you over the many hurdles to come.

As for your scheduling questions, much is dependent on your actor's schedules as well as your own personal preferences.

Four weeks is fairly typical for a straight play (non-musical) and it CAN be done!

Whenever I direct, I prefer to get the rough blocking done right away, usually after three or four rehearsals.  This gives you about a week-and-a-half to rehearse scenes, beats and business individually, refining the blocking as you go.

By the end of this process, (end of 2nd week) I  prefer my actors to be off-book.  (Some actors choose to do it ahead of time, but I don't require it.)  Unless it's a scene that requires a great deal of physical business -- a fight, a dance, the handling of many props, etc -- then I prefer them off book sooner for that specific scene.  This gives us then our entire third week to rehearse scenes off book.  (Of course, this happens only in a perfect world.  Actors are typically still calling for lines well into Week 3).

This Week 2/Week 3 is fairly flexible, but as we approach Week 4 we begin to incorporate costumes, ACTUAL props (instead of rehearsal ones) and before you know it, we're into Tech Week (Week 4) where we're dealing with lights, costume changes, set changes, etc. while trying to run the play from top to bottom without stopping.  (Actors DEFINITELY must be off book and forbidden to call for lines by this point).

The trick is to tell your actors you want them to be off-book by a certain date (and make that a date earlier than you really expect).  Actors love to have goals to shoot for and it gives you one less thing to worry about.

Best of luck to you!

Four weeks is doable but manic.    We do 7 - 8 weeks for our shows.  Part of our problem is depending on where in the season the show is we might only have four weeks to get a set built.   We're lucky enough to have our own space and have a rehearsal room at our disposal.  While one show is in production the other can be rehearsing.  The 2nd and 4th show of the season though always has a shorter build window which oddly enough hasn't stopped us from doing some of our more elaborate sets.

Good luck with your first directing foray!