Tamiya has a ton of variations on the F104 platform. This seems to confuse a lot of people, so I think a quick run down on what to use for what type of racing would be helpful.
First off, if you are running an "open" class, with no width or manufacturer restrictions, it would pay to look at a 3Racing F109, the F103 in it's various forms, or keep your eye out for a used Exotek chassis. These cars are usually faster than a narrow F104. They can also be cheaper depending on what model you buy. An F104W may also be a good choice, but the other cars are a little more sorted in wide form.
The HPI F10 can also be good for wide or narrow with an Exotek chassis. It may also take some more option parts to make it work in wide form from what I hear.
F104 Pro Black Special--Best deal hands down to run carpet on foam tires. Everything is in the kit. The regular Pro kit is ok, too, but you don't get the aluminum motor mount and aluminum pivot plate included.
Even on 3rd party rubber tires, the black car is the way to go. Pit Shimizu tires fit the stock foam rims.
If you're looking to go cheaper, or your racing rubber, the McLaren and Ferrari kits are not bad, but for foam you will need minimally a set of tires and wheels. The FRP chassis is stiff with the posts installed, and really the the only big disappointment is the friction shock. The TRF shock is probably the one must have thing. The motor mount is nice, but not something you HAVE to have, at least not right away.
With Tamiya you can be on the "option part installment plan", and add things as you go. This is not the cheap way, but it's cheap to start that way.
Obviously, no civilians have an F104X1, but it would probably not be bad on carpet for rubber tire with the long top deck. I guess we'll have to wait and see.
If you can wait a bit for an F104X1, it looks to be the premiere model for rubber tire asphalt racing. I have not done a ton of foam tire racing on asphalt recently, but it would probably be great for that as well, possibly with some changes.
The Pro or Pro Black special models have all the extras, but are a bit backwards for rubber on asphalt. You will wind up changing a lot of parts to build traction into the car. At a minimum, you would want to buy a split upper deck or cut the stock one to put more flex into the car. The other thing is that really, the stock graphite chassis is far to stiff for rubber tire. Not bad if you plan to race foam in the winter as well, but not the best deal overall.
The basic kits are actually a pretty good deal here. Really, a set of Tamiya option soft rear tires (under $10) and the shock are what you need, if that. The friction shock might not even be that bad, but limited spring selection is not so nice. However, the steel axle is a plus, FRP upper and lower plates, and the bodies that come with these kits have a bit more rear downforce. Not a bad deal at all, and you can add parts as you see fit.