You branch off from the copper tubing with a 1/4" compression tee. Cut out a small section of tubing for which the tee replaces. You must use a tubing cutter to do this, any other method will cause the tube to become oval.

Install the short piece removed on the side outlet of the tee. Attach a 1/4" compression x 1/2" pipe thread adapter to the short section. If you can find a tee with a pipe thread side outlet (preferred), skip the previous step.

Connect a 1/2" pipe thread to hose adapter. When buying parts, ensure the male and female parts mate correctly. If you can't find the proper mates, get a short nipple or coupler to change gender. Use several layers of teflon tape on male pipe threads, wrapped in the direction that causes it to get more snug when the pipe is screwed in.

Attach hose and controller. After all this, there probably isn't much pressure left, meaning you could probably transition from hose to 1/4" drip fittings for the run from controller to plants, keeping the installation less obtrusive. If you use pressure adaptive drip fittings, you can better regulate the flow to each plant, otherwise the first plant will get the most water, the last hardly any.

Be careful, though unlikely in this case, as high pressure can cause drip fittings to blow apart. You also can't use most pressure reducers, as they can spill water as they function. You'll probably have to go from hose to 1/2" drip main to 1/4" drip distrubution. The 1/2 to 1/4 punched connection can leak slightly, so it should be done over the first plant.

Cleaning the existing radiator is a good idea. Now, before replacing with baseboard units, a couple things to consider. You want roughly the same heat output rating (BTU/hr or similar), which may be difficult to calculate for the existing piping. (Any new basebord finstock will have its rating on the packaging). Most likely you'll need a long-ish baseboard run to match the existing radiator's output.
Unless you have cosmetic objections to the existing radiators -- and keep in mind you can probably buy different covers, or re-paint the ones you have -- you might as well stick with what you have rather than rerouting the feed&return pipes to fit a baseboard run.

BTW, if the wall behind the radiator is not insulated and preferable covered with reflective metal foil (to maximize directing heat into the room), you should do that.

edit

I looked up a few vendors of replacement covers. You will have to check the desired dimensions, of course.
improvementscatalog shuttershack .