Essentially the entry level HF rigs mostly fall in the $1000 and under range, and the pickings are pretty skimpy. Buying used can open it up a little bit, but at the risk of getting someone elses problem child.
The Icom IC-718 may be about the cheapest new radio you can buy that is all mode, HF, and 100 Watts. But, there are some drawbacks to it. The receiver is only so-so, particularly in packed band situations, and it does not include an antenna tuner. Still, for $700 or less ($650 to $700 in most stocking locations) it is not a bad deal. But remember, no tuner, and you are going to want one. So figure $900 or so to be realistic.
The FT-450 includes a tuner and is only in the $950-$990 range, and is a much better receiver.
The FT-857/897 include 2 meters and 70 cm, but again no tuner, and run in the $825-$980 range.
The Kenwood TS-480SAT includes a tuner, runs about $925 to $1000, and probably has the best receiver of the under $1k radios.
So, with a tuner, that leaves the IC-718, FT-450, and TS480SAT, and a price range of $900 to $1000. Personally, I would opt for either the 450 or 480 because of the better receivers, and I would be leaning towards the 480 as the more flexible design (remotable head in case you desire at some point to go mobile, or have an ops area with limited desk space) and possibly slightly newer technology over the 450.
T!