Also my strategy is get the best economy and steamroll the ai after a few hours
Generally speaking, if you're left alone to work on your economy, you should be able to have maximum-sized fleets, all important tech, and superweapons operational in under 2 hours. The best advice I can give is to get that economy rolling faster. Early-game fast colonization and mid-game trade-spam is the best way to fuel these late-game super armies, and get them out sooner.
TEC is more of a rushing faction. All their important techs appear at the lower levels of the tech tree, their units are cheap and easy to amass, and their economy gets rolling a bit sooner. While their economy stays top-notch into the late-game, they really don't have the vicious high-end combos Advent and Vasari can field and this reduces their relative performance later on. The goal as TEC is to get one step ahead of the enemy with your generally better cost-value, and then stay on top of the pack. In multiplayer, a TEC who falls behind stays behind; they can only succeed in the late-game if they're significantly larger and stronger than their opponents.
Advent... is a really fun faction, but the AI plays them like a dog. They have some very elegant and amazing combos that the AI just cannot pull off. This means you will never feel the true power of the unity in singleplayer. With all defensive combos in play, Advent can top out around 98% damage reduction. Needless to say, it's not unheardof for Advent players to win late-game battles against TEC opponents without taking a single casualty. Vasari on the other hand... is devious.
Vasari is your wicked faction with brutal special abilities that can really hammer enemies. However, their units generally are more expensive and less cost-effective than the other factions. This means they can be overwhelmed by brute force if they don't field the right specials. However, with the right abilities in support there's simply no safe way to approach them and they can torch fleets many times larger than their own. Most players agree that Vasari is the strongest faction currently, though I think TEC is stronger on the rush.
-How do get rid of advent Mines
There is no easy way. You can try just tanking them with capital ships if there are few enough mines. You can also inch forward with scouts (their "reveal" range is slightly longer than the acquisition range for the homing, so if you turn them to hold ground mode and move them forward slowly you should be able to reveal without triggering them) but this can be time consuming. If you can capture the gravity well, just build a trade port or refineries and let civilian ships detonate the mines.
-What are the best ship combos for each team?
For TEC, I'm a big fan of Javelis LRM / Garda Flak Frigate / Hoshiko Robotics Cruiser. Low-tech, cheap and easy to assemble, and absolutely brutal in a battle of attrition. Combine with strong military capital ships like the Marza and Sova and you're in business. The garda is only really weak to light frigates, which the Javelis LRM cleans up neatly. The Javelis is only really weak to heavy cruisers and strike craft. The gardas clean up strike craft, and heavies won't come out in sufficient numbers until much later in the game. The hoshiko is pretty much mandatory for any strategy except carrier massing, and is 60% of the reason to play TEC.
For Advent, the Seeker and the Disciple make a surprisingly good combo. Cheap and cost-effective, no research involved, and fairly well-balanced and tough. The Iconus Guardian and Progenitor Mothership are a must-have cruiser/capital combo that can vastly extend the longevity of Advent fleets. Also: Halcyon Carrier. It's carrying the Advent faction in the early-game currently.
For Vasari, you can't go wrong with an Assailant / Sentinel combo. It's not as good as the TEC version, but it's the same principle of combining two strong units to cover their mutual weakness. The Skirantra Carrier is an absolutely awesome capital ship, not to undervalue the other Vasari options out there. However, your best unit is the Stikulus Subverter, which can shut down enemy units and render them helpless. You can combine this with minelayers to lay explosive traps around them while they're unable to fire back, then sit back and watch the fireworks. Absolutely scary combo.
-Which abilities are best?
The Hoshiko, Iconus Guardian, and Stikulus Subverter stand out as top-notch support cruisers for their respective factions. For capital ships, TEC can get a lot of mileage out of the Marza (raze planet, missile barrage), the Akkan (armistice), and the Sova. Advent gets its best results from the Halcyon Carrier and Progenitor Mothership, while the Rapture is also a gimme late-game with its awesome Vertigo and Concentration abilities, both of which are uncapped and just get better as fleets get larger. The Vasari get a lot of mileage out of their Skirantra Carrier, but the Vulkoras is planet-cracker without peer and the Kortul should never be underestimated.
-If i play online what should i use?
Either a TEC Sova/LRM rush or a Vasari Skirantra/Assailant rush. Avoid Advent until you get some experience, they're very difficult to play effectively in the current version. The easiest tactic to pull off that can actually threaten a skilled veteran is to jam as much firepower down his throat as you can as quickly as you can. That means loads of LRM as TEC or loads of Assailants as Vasari, backed up by the carrier capital ship specced with combat abilities.