Cycling with fry is not an option. Use some mature filter media from your old tank or an LFS (transport it just as you would a fish in a bag of tank water) to kick-start the cycle. You'll need to put it in your new tank's filter and add fish within 2 hours if you want to avoid starving the bacteria though.
There's plenty of choices but if you're after something easy to look after with little maintainance I'd avoid tetras or any other schooling fish as it would mean you'd need more of the fish which would make your tank fully, if not over, stocked so you'd realy need to be careful not to slack on maintainance. I'd also avoid guppies which can be fragile due to over-breeding.
Dwarf puffers are an option but aren't particularly hardy. You could keep 2 in a 10 or 1 in a 5 but you'd want to plant heavily, feed small snails occasionaly and shouldn't add anything else to the tank.
3 FEMALE platies would be a hardy option for a 10 gallon - don't mix sexes as they'll have fry and don't get all males as they'll get a little aggressive.
Similarly, another livebearer, mosquito fish (females) - that is heterandria formosa - NOT the more aggressive and larger gambusia affinis - would also work. They only get to about (just under actualy) 1" so you could fit up to 7-9 comfortably. They do fine in slightly lower temps as well so don't require a heater if it doesn't get too cold. Watch that, as they are so small, the filter isn't liable to suck them up.
Endler's are hardier than guppies but not as hardy as either platies or mosquito fish. Still, they make a good choice as they are colorful and very small. With these, either go for a group of 4-5 MALES ONLY or 3-4 FEMALES ONLY. Females grow larger than males which is why I suggested the different numbers. Watch that you aren't getting guppy x endler hybrids (not because they are hybrids but because they tend to be heavily line bred - making them weaker).
Do you like gouramies? Honey gouramies (colisa chuna/sota) are quite hardy. A trio (1 male, 2 females) would work in a 10 gallon but provide quite a few hiding places - floating plants or tall rooted plants are appreciated but they need not be real. If you can't get a 10, you could keep a single male in a relatively heavily planted 5 gallon - just make sure of the sex as females like company and are not territorial so a 5's too small for them. Sparkling gouramies would also work in a 10 but are more fragile. If you went for just a single one, a 10 gallon could also house a paradisefish provided you were careful to decorate the tank quite heavily and vary the diet - more for stimulation than for health reasons as these are another remarkably hardy species that can even live without a heater (or even without a filter) if necessary (obviously it's best to provide them with heating if temperatures drop below 68 deg F though - at night or in the winter for example).
There's lots of tiny killies (like clowns) that work well in even a 5 gallon. Not all work and not all are hardy. Another I like, if you get a 10, is the american-flag fish. A pair or trio would be extremely entertaining if you provide plenty of hiding places AND they have the added benefit of being incredibly hardy and low-maintainance, non-picky, undemanding fish.
Alternatively, you could try keeping some shrimp or apple snails or another small freshwater invertabrate. You'd be surprised, when it comes to shrimp, how many different types there are - not just your typical ghost shrimp but vibrantly colored relatives and also giant filter-feeding species. Take a look here:
http
/www.petshrimp.com/index.html
Apple snails are also wonderful in that you can breed them easily and they come in all sorts of lovely colors. There's other ornamental snails out there as well. The downside to snails is that they produce quite a lot of waste and, apple snails in particular, get to about the size of your fist - making a 5 gallon rather small for several.
African Dwarf Frogs are something to consider then.
