First you need to make a decision on tires rubber or foam
Foam is definitely higher performance, but it also is higher maintenance, and can chunk as well. Rubber has an advantage in dustier or lower traction situations, but there are a lot of choices on inserts and preparation that make big differences.
Most racers racing TCS events have found that the Premounted tires that come with the 15th anniversary F103 work well on both prepared asphalt and carpet. HBR medium front tires are very similar to the Premount fronts, and have a similar performance. There is also a rear tire offered as a donut which is similar to the Premount rear, but this is increasingly hard to find.
On carpet, the kit tires from the F103RM are good as well. They are similar to a "gray" or "white" type 1/12 tire, in that they have a low rubber content. The rears are soft, and work well as an alternative to the Premount rear. The fronts are firm, but make a good tire for tracks that tend to "fuzz up" and cause tires with higher rubber content tend to pick up carpet fiber or debris and glaze over. The rears are also useful in this situation.
I have found the HBR soft rear is also a good asphalt tire. It seems close to a "pink" pan car tire. The HBR soft front works if your track is low traction and the car is too locked down with the HBR soft rear. Otherwise, the soft front may offer way too much steering.
For non-TCS situations, there are several tires that work well. The 3Racing F109 kit tires are actually extremely good, especially on carpet. They are also premounted.
TM Racing from Michigan did offer donuts in several standard compounds. Purple, Magenta, Pink and Green are all tires I have seen for the F103 sized rim. Magenta on 4 corners or Green on all 4 is pretty good for carpet. 4 Magentas can also be good for asphalt as well.
Zen out of Japan offers premounted tires in several durometers. Locally, racers were having good luck with 35 fronts and 25 rears. These are also the spec tire for the RC F1 GP in Japan.
The F104 is a trickier subject as Tamiya offers only 2 sets of tires for this model. The kit tire from the F104 pro is actually perfect for carpet racing. The "b" compound is really meant for asphalt racing with it's higher rubber content, but could be a choice for carpet as well. Usually, if the groove is up, the kit tires are the best choice. If you are racing outside of TCS regs, 1/10 pan car donuts, such as Windtunnel RC offers, are the correct size to fit the 104 rim. They will be much wider than the wheel, however, so you'll need a truer to size them.
The other option for 103 width cars is the Indy car wheel Tamiya made just for the Newman-Haas car. This wheel is about 10mm larger in diameter than the normal F103 wheel. This makes it not only perfect for 1/10 size pan car donuts, the larger wheel diameter makes the car easier to drive and provides a more positive driving feel. I have tested this back to back with the normal rims, and it is worth a tenth or two. This may not be legal for all races, however.
Rubber tires are a bit more limited on choices. The current TCS rubber tire car is the F104, and you are limited to the kit tires and the Tamiya "Option" tires. The kit tires could be described as a medium, with the Option front being hard, and the Option rear being soft. The most common combination on asphalt seems to be the kit front and Option rear (medium front, soft rear). For carpet, the jury is still out. Out of the package, both types of tire seem to pick up a lot of carpet fiber. Running the tires on asphalt, or using a tire truer to remove a thin layer of rubber seems to help with this. It may also depend on the track as well, or even the additive.
With rubber comes the question of insert. The stock insert fills the tire, which not all tracks may like. HPI Low Bounce or Yokomo Non-Repulsion type inserts work nicely on prepared asphalt tracks and provide a bit more air gap on the tire. Cut down diameter sedan inserts are also very good on high bite tracks, but the car can become overly nervous if the traction is not high enough. No insert at all has been tried as well, but the results may vary. Covering the vent hole or making it smaller may be an advantage when trying to run without inserts.
Outside of the Tamiya tires, the Ultimate F1 series drivers from California report that Pit Shimizu tires are working well for them. This page details what they have found on the Pit tires, and others. If you run the HPI F10, not only are the HPI branded Ride made tires available, tires and wheels made for the Tamiya F201 4wd F1 will fit as well, but the Tamiya wheel must be used. Ride tires are about the only choice for the F103 style cars. Tamiya did make rubbers for the F103, but they are discontinued and hard to find.
