Just getting started on a budget and need bookshelf speakers/receiver now

Check out Air Pulse Active Speakers by Phil Jones. 

Go listen to the small Ushers S-520. Also there are multiple KEF, Paradigim, and the list goes on. Your ears will tell you what you like, and so much is based on the equipment that is plugged into the wall. One thing I find is the equipment built for theater AV will not be as pleasant.  From what I am told that to get the licensing for things like THX, Dolby and other AV system requirements that they list on the front the company pays a handsome fee and so to keep the cost of the unit where they need it, they sometimes cut the corners on the materials.  If this is just for music try to avoid the theater based electronics.

I likely would put a little over half into the speakers and then work on the electronics as a rough start although you may find a bit more goes into the speakers in the begining. So replace the infinity first. And just because equipment is old doesn’t mean anything with some companies. I know people with very old equipment and incredible sound. Do you have a good place to go listen? Some high end shops do a used or consignment. And remember to let them know your room characteristics. I have seen Totem, and Vienna that you can get for that kind of money in used speakers, and depending on how they were used they can often sound new without the break in period. Just be a smart shopper and ask questions. You can also look online at places like US Audio Mart, or on this sight in the selling section.

It is not just how much you spend, but how you match your gear. You can spend thousands and still have mud. I have a pair of KEF 350 as one set and they were around $500. They aren’t amazing, but in the room they are in they work well. I also have an older set of Paradigms that I like for more classical and folk. You can find something just do a little research and get your ears to a shop if you can.

Unfortunately, I haven't found a place where I can go and listen.  They are either home theater companies or Best Buy.  Nothing in between.  But I'll keep looking.  It sounds like the ones I listed are really a no-go so that is good to know.  And I appreciate the suggestions.

Used NAD receiver ... and used Monitor Audio Silvers ? 

Legacy focus HD used?. I have seen up for sale. good luck.