Vacuuman

The bag in the picture of the machine was a Simplicity High-Flow HEPA.  These bags are made from the Filtrete material.  Filtrete and High-Flow HEPA are the same.

I would suggest the Riccar or Simplicity for the price you are looking at.  For a good quality canister, you really should go with a Vac Shop brand.  I would also avoid any bagless machine if filtration is important, as they tend to be very dusty messes.  You also need one with a electric powerhead for the carpet.  All canisters typically come with floor tools, and also have mini turbo tools available for stairs/furniture.

There are some excellent vacuums in your price range, and the best place to get these would be a local vacuum store.

My personal recommendations would be to look at Sebo, the G1 and Simplicity Synchrony/Riccar  Brilliance.  These machines are some of teh best on the market and are very well made.  I also recommend these models specifically because tehy use permanent belts that are guaranteed by the manufacturers to last the life of the machine.  The advantage of this on pet hair is that the brushroll will always be turning at full speed to make sure that you are picking up well.  Vacuums that use stretch belts tend to lose efficiency as the belt begins to slip, a vacuum with a permanent belt will not do this.  These machines also have very good filtration, the Simplicity even has a charcoal filter to help keep any pet hair smells from comong back into the room.

My opinion, for what its worth.

No big box store machine is a true HEPA vacuum, you will only find these in the specialty stores, and on brands such as Simplicity and Miele.  The Simplicity Synergy has 2 levels of filtration, standard and plus.  For lead I wouuld suggest upgrading the model you are looking at to Plus if you choose that model.  The Hepa Plus filter with the sealed system gives the vacuum a rating of 100% (tested with the particle scanner thing) of all particles down to .3 microns.

But like some others here have said, you need to see if the Synergy is the right one for you.  It would be a great vacuum for a house with all carpet or mixed carpet, rugs, floors.  For all bare floors with a few areas of carpet you may want to consider something else, like a suction only HEPA canister, or a canister with a mini power head if you have larger area rugs, or 1-2 small rooms of carpet.  The best way to go is to go to the vacuum store and be specific, tell them you need HEPA and describe the house you will be cleaning, such as floor surfaces and other things like if you have pets, and let a experianced sales person help you decide what features you want/need.  And you can try them out while you are there.

In my opinion, M.D., Cyclovac, or Vacuflo.  Cyclovac makes various other brands like Riccar/Simplicity, Star Power, and a few others.  I personally have the largest of the Riccar units and love it, by far one of the best units on the market.