Hmm... There appears to be no tonnage limit and no problem with selectively moving stuff if it's within a light second. Note that one light-second is one heck of a short distance by spacial terms, the sun is 499 light seconds aware, so we're going to be somewhat limited. Even many satellites are over a light second away. We're not going to be able to move much. Most stuff will have to be built on earth. Even a geosynchronous orbit is about a quarter-light second so you can see how utterly close that is. We can't even affect the moon until we get into space proper.
So the goal is to expand to other planets.
First, demonstrate I can teleport objects to the relevant authorities. If it still exists (most don't) collect on whatever magic/supernatural power contests are currently running for prestige and pocket change.
Invest earnings into life-extension for myself. I'm the most valuable person in the world right now.
Arrange for multiple independent teams, ideally in independent countries, to verify plans. Once multiple independent teams have confirmed it's a good idea, proceed with plan at each stage. We don't need to accidentally destabilize Earth's orbit by moving too much.
Teleport in chunks of asteroid and comets as needed. That will only work when objects of interest are close, so arrange for massive observation of space and space stations in place so I can move to them. Since I don't have an effective mass limit, I may need to arrange for daisy-chains of stations so I can move rapidly between them and teleport asteroids and comets daisy-chain 1 light-second at a time to get them into position. I can't teleport myself or other humans, but I can teleport hydrogen directly into fuel tanks for high-speed travel at max speed.
Have teams create segments of a space station, as large as can be reasonably constructed on earth. This is going to require waiting for asteroids and comets to move into 1-light-second range, which isn't common, so promote tracking every last blob in the solar system and building aforementioned daisy-chain to move them one lightsecond at a time into orbit.
Teleport Space-Station segments into space as needed.
Teleport fuel into the rocket as needed to get it into space and get vetted construction workers to assemble the chunks as needed. Send scientists and whatever else is required as needed.
Arrange for the creation of a Lunar space base. I don't need to build it myself though I'll teleport in nearby asteroids for materials as needed using the daisy-chain.
Teleport fuel into the rocket as needed to get it into space and get colonists on the moon.
Even the moon is 1.28 light-seconds average, so we can't touch it yet. Teleport the base to orbit, then alter its trajectory at the moon as needed. Once that's done, travel into orbit so that my range is effectively 21LS from Earth, then transport pre-built modules to the moon as needed.
We can't fix Mars... yet. It needs a stable atmosphere and it's well out of range.
However, once you're in orbit, you're halfway to everywhere else. Teleport fuel as needed to the space stations, then send them to mars to assemble a colony. Once a daisy-chain of stations is assembled, travel to Mars and beyond.
Teleport nickel-iron asteroids into Mars orbit using the daisy-chain.
Replace Mars' core with nickel-iron to create a planetary magnetic field, teleport its core into orbit to produce a decent-sized moon.
Reeee at the scientists who probably didn't get it right the first time and redo as needed to give Mars a planetary magnetic field. Look, this is uncharted and hideously complex work, it probably won't go right the first time.
Teleport comets as needed to give Mars at atmosphere once it has a magnetic field to contain said atmosphere.
Have rocket scientists design cloud cities for Venus. Alternately, have them draw up plans for how Venus might be terraformed by teleporting greenhouse gasses out of it depending on prevailing models. Teleport out greenhouse gasses
Repeat Martian plan with Venus. Reeee at scientists who didn't get it right and redo until Venus is inhabitable.
Construct further Daisy-Chains of stations to the Oort cloud until I can access comets a needed.
Begin construction of long-range probes, and then ships, to reach other solar systems. These are vastly outside my reach telekinetically but once you're in orbit, you're halfway, there, especially if I can use daisy-chains to get a full load of and move myself at top speed using max fuel along the way. I can always teleport fuel in as long as it's within a light second, so build fuel-stations every light second. Spend time moving massive, quadrillion-ton fuel canisters back and forth (after teleporting comets to refinery stations we teleported in to make said fuel, of course) to ensure rockets have massive fuel supplies in place to let them burn at 1G for long distances.
At 1G, We're looking at three and a half years to reach Alpha Centauri. However as they slowly orbit, the daisy-chain will make other systems that are further away accessible too.
The expansion will continue until I die of old age, which will be as long as the finest medicine humanity can possibly create given I'm the single most valuable person on earth at this point and I began pouring billions into life-extension early on. If things go well, early investments into life extension pay off and we get this rate of expansion for 100-150 years. If things go exceptionally well, we figure out centuries-to-immortality but I won't count on that. If not, spend my last years building infrastructure to make expansion easier once I'm gone. Arrange for a statue of myself at the vastest size possible to be built because I still have an ego.