Note: It depends what ecosystem you're creating. A planet will have very many sub-ecosystems but some basic commonalities of interdependency.
The absolute minimum may well be down as low as half a dozen, if the colonists are prepared to eat basic yeast-algae based slop, but the greater the number of species, the greater the ultimate stability of a system.
Given time, creatures will evolve to fit niches in the world that are unpredictable. Again, the increased occurrence of this will promote the chances of resilience against extra-seasonal variations caused by eccentric orbits, freak weather, unexplained population collapse.
The species below represent a stab at a general ecosystem. The numbers represent the number of species. The number of genetically distinct individuals in each species would vary. The minimum viable population will vary greatly by species, some only needing hundreds, some many thousands. The fewer supplied, the greater the chances of the population suffering failure through lack of variability in the genome (and the physiological/behavioural and immune-responses of individuals).
The machine, being a quasi-omnipotent AI would need to constantly monitor the balance and make adjustments until the system showed signs of homeostasis without too many wild swings - and step in again if things needed adjusting.
First 1000 years:
Cyanobacteria. Initial oxygen production. (~10 species) The species number will increase as niches are colonized over time - allow for mutations and speciation at this stage.
Nanophytoplankton. (~10 species) Carbon fixation in oceans (chalk formation etc..)
Nitrogen fixers. Converts gaseous nitrogen to various salts available in the water-table. (~5 species)
1000 - 50,000/100,000 years:
Algae. Greater oxygen generation capacity, more biomass generated. (~5 species)
Fungi. Breaking down dead biomass. (~5 species)
100,000 year point:
Land:
Tough grasses. Soil stabilization and creation of humus in decomposing. (~5 species)
Flowering woody-shrubs, trees. Carbon fixation. (~10 species)
Fertilizing insects. Apis melifera (honeybee), bumble bees, ants, wasps. (~20 species)
Butterflies, moths. (Aesthetics, pollination.) (~20 species)
Worms - earthworms and various nematodes and flatworms (land and aquatic). Soil creation and improvement. (~30 species)
Mosses, lichens, ferns and Worts. Humus creation and spreading biomatter over inorganic substrates - paving the way for larger species. (Plus, they're laying down peat should the future need it.) (~20 species)
Slugs, snails. Turning organic matter into altered biomass, stimulating plant growth. (~10 species)
Flies. Dragonflies. Spiders. (~20 species)
Termites. Increase wood breakdown. (~5 species)
More fungi. Cellulose breakdown. (~5 species)
Tardigrades in the soil to deal with the tinyest fragments of cell-debris.
More bacterial strains (land/water): Rhizobium leguminosarum, Pseudomonas putida, Bacillus subtilis, Desulfovibrio desulfuricans, Actinomyces israelii, Bacteroides fragilis, Geobacillus stearothermophilus, Methanococcus (Methanocaldococcus) jannaschii - This list of 8 strains is provisional and I will update as I can. Given the timescales and bacterial reproduction/mutation rates, I would expect hundreds of thousands to millions of strains to be available around the 1 million year mark.
Sea:
Phytoplankton, small shrimps. Corals for more carbon-fixation. (~15 species)
Multicellular algae. (~5 species)
Kelp, sea-grasses. (~10 species)
(Aquatic) Slugs, snails. Turning organic matter into altered biomass, stimulating plant growth. (~10 species)
Echinoderms (urchin-family) and bivalves. (~10 species)
500,000 year mark:
Land:
Flora:
More flowering plants. Squash, legumes (nitrogen fixation by bacteria in root nodules) fruit trees, nut trees. (~20 species.)
More grasses. Maize, barley, wheat, oats, wetland grasses, reeds etc.. (~20 species)
Fauna:
Herbivores, mainly small grass-eating. Hares, rabbits, deer. (~5 species)
Carnivores. Foxes, eagles. (~5 species)
Omnivores. Small rodents - mice, voles, shrews. Chickens, pigeons. (~10 species)
Ophidians (snakes). As poisonous or not as you like, keep the rodent population down. (~10 species)
Beavers and amphibians. Wetland species will begin to thrive. (~5 species)
Sea:
Fish. Minnows, bream, bass, ray, tuna. (~10 species)
Shoreline. Muscles, limpets. (~5 species)
Larger shrimp, crabs, squid/octopus. (~5 species)
950,000 Year mark:
Caprinae (goats, sheep). Great for varied landscape and produce milk and meat. (~10 species)
Bison, wolves, camelids (as pack animals in various terrain), medium-sized cats. (~10 species)
Corvids for scavenging. (~5 species)
Sharks, eels, salmon, carp, catfish. (~5 species)
Cockroaches. (Yep.) (~5 species)
Small birds. Finches, tits, basket-weavers, songbirds. (~10 species)
To improve the livestock and ensure immune-fitness, a number of parasites (ecto and entero might be introduced). Mosquitos, horseflies. Bats would come in handy at this time. (~30 species)
Note 2:
It may be necessary to reintroduce species that have fallen to over-predation and catastrophe - the perfect storm can ruin any plan, so corrective measures should be able to be taken. In an idealized scenario, the AI driving the terraforming would be able to compensate for minor changes to genomes such that any unexpected aberrations through mutation produced strange forms that threatened the stability of the whole.
There is also no reason not to include any species you fancy. For example, elephants are great clearers of new-growth and will devastate woodlands wherever the herds wonder, but maybe that's an effect you want.
I figure that a few alligators in the fresh water lakes/waterholes/rivers in equatorial regions wouldn't go amiss, but I leave that to the discretion of the worldbuilder.
Aquatic mammals tend to fit at the top of (or somewhat adjacent to) food chains and can be added at the discretion of the w/b during the latter stages, let the fish-stocks build up and stabilize first.
Note bee:
Honeybees don't have much by way of an immune-system of their own. The immunity that colonies have they gain from the various trees, shrubs and plants they visit, using Phyto-chemicals to ward-off infections and parasites. The greater the variety of trees and flowering plants, the more chance of bees flourishing and getting the job done.
1,000,000 years:
In real-life, Hominidae, the family containing us, produced the last common ancestor of chimpanzees and humans (Hominini) roughly 10 million years ago, having split and the ancestor disappearing perhaps 5 million years since. Lucy (Australopithecus) dates to around the 3.2 million year mark. Homo arriving on the scene around the 2.75 million year mark - in many varieties.
The "mitochondrial Eve" from whom all women descend is estimated to have lived 155, 000 years ago. Y chromosomal Adam (from whom all men inherit their Y chromosome) somewhere between 200,000 and 300,000 years ago - which roughly coincides with the advent of physiologically modern humans.
If you want humans to evolve, then you need a much longer plan. Alternatively, print them whole at some suitable point in their ancestry. We modern humans are thought to derive our existence from repeated mixing and separation, then mixing again between all the many, many separate lineages with each mix altering the genome and the creature you'd see.
You've a whole menagerie to chose from to create the finished product with at least 8 different distinct lineages of Homo going into our makeup in varying amounts at different times.
- Additional Homo varieties: ~8. Possibly more variations by height, pigmentation etc..