The blu ray burner that most would recommend is not a very inexpensive one. It is the Pioneer BDR-205BKS: http://www.newegg.com/Product/Product.aspx?Item=N82E16827129051
If that is just completely out of your price range, there is this LG for sixty dollars less: http://www.newegg.com/Product/Product.aspx?Item=N82E16827136181
If you don't intend to burn blu ray media, you don't have to have a blu ray burner at all, just a blu ray rom drive. You might want a combo drive that can only read blu ray, but can read and burn single and double layer dvds Here is an example at Newegg: http://www.newegg.com/Product/Product.aspx?Item=N82E16827136195
There are several more BD combo drives available there, from manufacturers including LG, Samsung, Lite-on and Asus
It is possible to back up blu ray movies. You'll need a decryption program for this. AnyDVD HD and DVDFab are two good choices. DVDFab has a section within it called DVDFab HD Decrypter. It will continue to function as a decryption/ripping program even after the trial for the main section expires. The only caveat is that it will lag behind the commercial version by 8 weeks or so on decryption updates.
The other program you'll need is BD-Rebuilder, which is free. I wrote a guide for it here: http://club.myce.com/f142/bd-rebuilder-guide-313227/
BD-Rebuilder can compress a blu ray movie to fit a double layer or single layer dvd. The format will still be blu ray (AVCHD compliant), so you'll need either a blu ray player to play the movies, or play them on your computer with the appropriate software. If you are considering making backups to dvds, be sure that your current (or future) blu ray player can play AVCHD compliant disks. You might want to look through this entire thread at doom9: http://forum.doom9.org/showthread.php?t=144674
You'll only fit one blu ray movie onto a single layer or double layer dvd. The average blu ray movie will be over 30gb, and those target sizes are 4.3 and 7.9gb. That is quite a lot of compression. The double layer backups look very good by the way.
BD Rebuilder can also output to fit 25gb blu ray blank media. This is my choice for backups. Of course you'll need a blu ray burner for this option. I suggest Verbatim brand blu ray media, though I don't recommend their LTH variety of blu ray disks unless you are absolutely certain that your burner and all your players are compatible with those organic dye blu ray disks. The Verbatim LTH disks do tend to be less expensive.