Radial or cross ply/bias ply? The radial construction has a very flexible sidewall but a stiffer tread area. The cross-ply construction has much stiffer sidewalls with a more flexible tread area. Radial tires are designed to be fitted tubeless and cross ply are tube type.
Spoked wheels like those on the CPI SM250 are not air tight so you must use a tube. It is possible to buy a kit that fits within the rim that makes it airtight, quite expensive and reliability is not assured.
Another issue is that the edge of the rim is designed to hold a cross ply in place and not a radial tire. Combining a Radial tire and a tube may lead to slippage and blowouts due to the flexibility of the sidewall on radial tires.
With a width of 2.75 front rim 3.5 back rim there are not all that many choices for tires. It is equipped with Maxxis excellent cross ply promax 110-80-17 front and 130-70-17 rear.
Going wider will cause the tire to touch the forks in the front and the chain and swing-arm at the back.
That should be all the info you need to make your choice.
Front: On the front I fitted the 110-70-17. This gave me a lower profile which gave me more precise turning at the cost of a harder ride. Incidentally this lessened the head shake by causing the bike to be lower at the front thus putting more weight there. It also meant that the tire itself would wobble less giving added stability.
Maxxis
Bridgestone
Back: On the back I fitted the exact 130-70-17. However, it would seem that Maxxis and Bridgestone do not agree on the size. The Bridgestone rubbed against the chain where the Maxxis would not. This is no doubt due to my weight and the Bridgestone having a more flexible tread. I solved this by turning the axle very slightly so that the front of the tire cleared the chain. Blue/white rider Bridgestone Black/orange Maxxis.
These are not the SS racing tires but I used them for track days anyway. The front tire was outstanding but the back was not. The rear tire over heated very fast and became very slippery. So for the race day I used the Maxxis again which handle the heat wonderfully. Aside for that I use the BT-39’s daily and you can feel the difference in handling, stability and comfort.