Ideal Method for Movie Collection/Storage?

I would like to start collecting some of my favorite movies to watch at my leisure.  

I did a little bit of research but wanted some different takes on this.

If you were starting a similar collection from scratch, what medium would you use?

DVD's or digital format?

I have a new nice DVD player.  I have Apple products.  Macbook Air with no disc drive.  iPad.  iPhone.  I also have an Apple TV but it's become fairly dated.  

I have no particular interest in watching these movies on any of my devices...just my TV.

I'm on a tight budget so money DOES matter.  I know the digital formats are more expensive.

I guess my concern is that I will collect a bunch of DVD's and they will soon become obsolete.  

What would you do?

TIA so much!!