To start planting it is wise to have some plan, and start with the low plants up front. Before you start planting put just enough water in the tank to completely saturate the thinnest areas of substrate, which is usually the foreground areas. As you move up the slope of substrate to midground and background plants add more water so that the areas you are planting are just at the waterline again. This will begin to submerge the previous planting areas. Keep a spray bottle handy with clean water to keep the plants not yet submerged wet as you work.
If you tie epiphytic plants such as java fern, moss, anubias to wood or rocks that can be done at any time, and may be easier to visualize the space for those so later substrate plantings don't get shaded by them if you put them in last. Again keep them moist with the spray bottle.
It would take getting everything just right to be fine adding fish right away, but it is possible. It would be wiser to start adding fish after a day or two. I'd wait long enough for stem plants to straighten up and orient to the light before you add fish. You have more water quality help with growing plants so you can stock the tank faster. I still like to spread it out over a week or two. That lets me observe what I have and gives a chance to see if the level of activity has the appropriate room as each group of fish is added.
As far as algae is concerned there will be some. What algae you get depends to some degree on what isn't being made available to the plants. Each algae has it's niche, a set of conditions that favor it. Those conditions tend to be the lack of something plants need: 0 phosphorus available is conditions for the green spot algae, 0 Nitrogen available is conditions for cyano called blue green algae, others gain entrance by an insufficient carbon source. Yes having a clean up crew is helpful but first make sure you aren't making conditions unfavorable for plants which gives entry room for algae to take over.
If you have the above covered so you have happy plants then the clean up crew will be able to handle the algae that does grow. Snails may be part of that, but you don't have to use them unless you like having them. Ottocinclus, nerite snails, and amano shrimp are the smaller tank best cleaning crew. Assuming you won't have fish that would bother an otto those very recommended in a planted tank, but the others are more up for consideration depending on what else you want to put in the tank. Some planted tank safe fish would eat snails and/or shrimp.
A hospital/quarantine tank becomes more needed if you consider shrimp or snails, because some of the medications you might use to treat fish would kill the invertebrates.