Depending on your band you can use LMR-400 or 240. To join your cables do NOT use PL-259/SO-239. Us an impedance matched connector such as an N or TNC that is more waterproof and add additional weather proofing. Better connection and much less loss.
Probably would be best to have the jumper at the radio end for several reasons. First, it's indoors (most likely) so weatherproofing won't be an issue. Second, since it's LMR-400 and quite stiff, a short jumper is probably best anyway to reduce the strain on the radio's antenna connection.
While it may be best to use a specialized connector for the joint (like a direct mating connector to what's already on the coax). Best case is your LMR-400 already has an male "N" connector and then you can order your jumper with the female "N", but if it's already got a PL-259 and your jumper does as well, just use a standard barrell connector and call it a day. If the extra .25 dB is that important, you need to run a new feed with the correct length and use something better than LMR-400 anyway.