Definitely better to leave open squares.   When you're first colonizing planets at the beginning of the game, you don't have the money.  And, you have to pay maintenance on the labs/factories you build.  Generally you want to get a Starport (no maintenance) and a Recruiting Center up right away, and get factories and research labs up on the bonus squares.   Fill up the planets later, when you have more money.

Or you could build economy structures rather then leave the planet idle. Personally i never leave a planet not building anything. But i think I'm in the minority there. But if you have the planet filled with facories and labs, you may need to change. I tend to have at least 30% of my tiles with economic structures; except for the tech capital and the manufacturing capital.

If you're that early in the game that money is such a factor, then i think you may be wondering more about how much to fill up the queue with improvemnts. Generally i never get more than 2 or 3 improvements placed on tiles. That way you don't have to mess with the building queue too much when things change.

I typically get a star port and a recruitment center (like tetlytea said) on the planet and then have it build colony ships.  Even though the planet doesn't have the population to fill a colony ship to the brim, it can at least make them and toss some people on it.

During the colony rush it doesn't matter how many people you got on each planet, it only matters how many planets you grab.  So I typically don't mind having tons of 20mil pop planets since I know they will all grow up to make my empire better than a few select 2bil+ planets.  By having each newly created planet making another colony ship, you exponentially expand until there is nothing left to grab.

Try to experiment here and there.

For instance, on tiny maps with few planets, you may find that the only way to ensure you are able to nab some of the few planets up for grabs, you might need to rush buy colony ships. The question is do you pay all of it now, or pay some now and a lot more latter. The first option saves you money in the long term, but drains you early in the game when its difficult to make money. The second option may save you money so you can do stuff that requires money, but you might quickly find that the weekly bills to be quite crippling on your economy.

Another case might be a larger map with plenty of planets. In such a case, you might find it productive to build sensor ships and use them to search the map in a methodical manor (starting with local space) so you eventually have seen every single parsec. The advantage of this is, you will likely notice nearby, but easily hidden galactic resources that you can exploit to give you an early advantage. It will also helps save you from one of those "feeling stupid moments" because one of the other civs nabs a resource near your homeworld that you didn't notice before.

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Me, one of the tricks I use is to send my space miner to nearby star (hopefully adjacent sector) to get an early glance of colonizable planets. After seeing the star, I can get info on the number of colonizable planets the star system has, and from there I can look at the planets to see the PQ and planet type. Once I'm satisfied with what I know, I send the space miner back home to start its mining operations (usually when I have a proper sensor ship to replace it).

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By the way, 2 tips: First, leaving your taxes at 0% is ussually an easy way to get 100% morale, which doubles population growth rate. The other tip is to never leave your tax rate siting on a multiple of 10. Increasing your taxes from (X0 - 1) to (X0) results in a larger morale drop than increasing your tax rate from any other number. As such, you should try to use tax rates like 39%, 49%, 59% etc. so you can minimize your overall impact on morale.

Just to add a bit to DW's post: When I colonize, I set the starmap to display only planets, not stars. You do that, and you won't have to bother with empty stars. Then I start the colonizing, going for the systems with the more planets first.

TA is the key term there though.  Back in DL/DA it was possible to do that.

It's all about timing. When you set the build queue for a new planet, put a market center or something at the top, then start building the factories. Depending on what your sliders are at, this will give the planet 10-15 turns to grow before maintenance-heavy buildings start appearing. It's not fool proof, but it's good for the absent-minded like me, who partially build a planet, then realize they never went back and filled it

Assuming that formula is accurate, the constant in TA is closer to 17. I just ran 3 planets and they all came out different, from 16.5 to 17.2

I don't see anywhere in the formula where rounding would cause that sort of variation.