A good start for HF could be an Off Center Fed, or an End Fed antenna. In fact two OCF antennas perpendicular to each other will help with directivity for TX and RX. Avoid various HF verticals that offer multiple bands without requiring numerous radials. Much depends on how much money you want to throw at it, such as a tower, rotor, and more money for a better antenna. Based on your request, working HF is not something you often do. I recommend one of the wire antennas I noted to get started before dropping
plenty-o-cash on improved equipment. You can find Off Center Fed, or End Fed antennas that will handle various bands from 160 to 6 meters. I am more of a fan of OCF antennas at home, but like end fed for portable use. Besides an OCF antenna, I also use a Hexbeam which is a multiband antenna. My K4KIO hex handles 20, 15, 10, 6 and one of the WARC bands. This antenna uses a rotor to direct RX/TX and works well enough for me. I purchased it used and shipped for a very low price. It performs well for what it is and it is worth full retail price to me. Still, there are bigger, better and more costly antennas.
For VHF/UHF on that radio you can use a single dual band antenna and a diplexer to feed the ports, or use separate antennas. You could even use switch and go from using an omni directional antenna, to a Yagi, or Satelliete antennas depending on what you want to work.
You requested most effective and that's fine if you want to throw money at it right away. A solution may be to use a high gain omni directional antenna and then switch to a Yagi and use a rotor to improve TX/RX as you dial the directivity in. Dedicated antennas for the VHF and UHF bands would be a step in the right direction whether omni or a directional Yagi as the TS2000 has dedicated ports for each.
Coaxial cable is also just as important. For HF I use LMR-400 which some may say is overkill. I also use LMR-400 for VHF/UHF, but LDF4-50A 1/2" Heliax is an improved coax, especially for UHF. For that I use pliable patch cables that are easy to manage as the 1/2" Heliax is rather stiff.
Take your time and keep asking questions and reading up. Remember, everyone's location is different. What works well for me may be worse, the same or better at your location. There is no "one" antenna solution. Well, there is this antenna at the
Titan Missile Museum. I have worked stations that were using the antenna over the years. I plan on driving, or flying and rent a car for a few days and enjoy using that antenna myself. Something to do.