Seems kind of interesting that you seem to kind of lump "digital" with "lcd/dlp projectors". As you start reading more, you will soon learn that when a theater advertises digital projection, they are not using a DVD player and an lcd/dlp projector. There are a few theaters around the country that do use DVD's with some kind of video projection, but they are at the opposite end of the spectrum in cost from the the digital projection systems advertised as being used at major theaters. The last time I saw someone discuss the price of a digital projection system on this forum, seems to me they were hoping the price would fall soon to around $62,000. Then there is all the rest of the equipment and facilities you need. So, digital projectors aren't usually for the low cost startup. If you truly have the capital, then maybe you won't mind the high price tags. Just make sure your business plan is feasible. Otherwise, you will make a small fortune from a large one.
If you decide to use the lower cost projectors with a DVD player, you will be faced with several challenges. New releases are usually not available on DVD, except in the cases of some small independent films. You said you want to be 2nd run, but even 2nd run films are not normally available on DVD. The few theaters who do this kind of thing are normally playing stuff that's been out for a long time and already released on DVD to the public. They are often revivals of classic films. Some use these to supplement their film line-up and don't rely on them for all their business. The ones I remember that rely completely on DVD projection are normally more like a cinema cafe or cine-pub.
The reason high dollar projection systems are needed to do the digital presentation you hear about is that the image quality has to be far superior to a DVD. DVD projection is better left to smaller screens, although some might argue they may be passable for a medium sized screen. Still, they will not likely be nearly as clear a picture as film projectors will put out. If I remember right, the high dollar systems use either satellite download or they ship special hard drives. It would take many, many DVD's to hold the same amount of data.
Oh, one more thing about playing movies from DVD. Don't forget you still have to make arrangements with film distributors to play them and then give them a percentage of sales or possibly a flat fee. It's agaist the law to play them otherwise, unless they are public domain. Most public domain films are moldy oldies that would draw little interest, although some are good movies. Those good public domain movies are probably available for $1 from the local bargain store, so anybody who likes that kind of thing already has them at home. If people would come to the theater to see them, it will be because of the experience you can provide and not the movie. Will your cheap seats and associated decor provide a great experience? Will you be serving great food, or just run of the mill snacks? If great food, then can you compete with other restaurants in the area? Will you have table service? Then your business will be a restaurant more than a movie theater.
I point out all these things because I've investigated all this stuff for myself over the past few years.
My advice is to go with film if you can. If you can't, then you need to rethink those cheap seats, and all the business plan that goes with them.