Let's all tread carefully in this thread, because I can easily imagine it getting locked.
Unless you are just going to do 'disk backups' and just keep them on the hard drive as an iso when you need them, you won't get the menus.
Best way is probably to strip out the vob data episode by episode, use a muxer to put everything in an MKV, and just label the files well.
The current WDTV (the new model of the WDTV Live) is likely the choice for you if you want to watch them 1:1 with no potential issues cropping up.
Amazon Link to current WDTV Live
Doing it on the Roku will require a live transcoder setup. There isn't any official Roku channel that can do that. There are a few unofficial ones, but at any time Roku could in theory kill that channel and therefore break what you need it to do.
WDTV would be better in your case because it does have the codec support internal to the device, with built in Wifi if you want to hook it up to a network.
I've set up most of the potential variants for 'media on the tv' type setups. My personal setup doesn't include one (because I have a more detailed setup) but WDTV is the best choice for 'it just works' and 'it just works well.' Outside of a few issues that likely won't crop up for what you are specifically asking for, it'll be the perfect setup.
The Roku honestly won't work well for what you want.
The other method would be to use a program that can be used to rejigger the VOBs and you could name them and put them on a hard drive. The issue there is, the PS3 is ludicrously picky about stuff. I've seen media servers specifically setup to stream to the PS3 sometimes fail on occasion. It's generally better to get a media player that can just do it properly.
Truth be told you honestly don't need them to be 1:1. Transcoding from DVD works relatively well for home use, and you can tweak settings relatively quickly and easily to make it look identical, even if you don't save much in the way of filesize. But I'm not recommending any of those methods since you asked for no reencoding.
Best method is still most definitely getting a competent standalone media box. They generally work quite well, are relatively affordable, and the good ones even add features as time goes on.