I read somewhere that mini light strings are wired in series and they don't get a long with LED's
Both ends are still going to be parallel. 120vac in 120vac out. Or are you talking about the individual bulbs? Most leds don't have changeable bulbs, which is kinda annoying, since half the fun is buying a bunch of sets then making different color patterns by changing bulbs around.
I do like to full wave rectify LEDs as well so the flicker is not so bad so I make sure not to plug any loads at the other end that won't like DC power. Eventually want to look at making a 120vdc SMPS that produces a smooth voltage to remove the flicker altogether, even at 120hz you can somewhat see it. You can add a capacitor to 120vac but you will get 170vdc which might be too much for the lights as they are designed with half wave 120vac in mind so they are probably underspec as is for that voltage.
This is how a typical light set is wired:
Had to rewire one to make it DC compatible as not all sub strings will be the same polarity, that was fun...
The longer the set the more series strings there will be inside, but the plug on the end is just a regular outlet as there's always two wires that just pass right through as the sub strings tie in to them. The limitation to how many you can plug in one string is the gauge of the wires and ability to handle the amperage from whatever is at the other end. If you are going to put a lot together, make sure the thicker ones are first as they will be carrying the most current. Though thickness is not that great of an indicator since it might just be thicker insulation. If it specifies the wire gauge then go with that. I don't imagine most sets are any more than 18-20 gauge though so I would not put more than like 5 amps through a set to play things safe. With LEDs you can go a long way though.