How do you deal with LRMs then, epecially having the mothership and all? Should I rush with deciples? Should I wait and tech illuminators and defense vessels or what? I heard defense vessels are a soft counter for LRMs, but if he targets only my mothership, you can't exactly get rid of the target. I know fighters are the best counter against LRMs, but how do I get them near him when he has a lot of flak?

A) Illums destroy LRMS, in the battle of lrm vs illum, illum wins

Illums Counter Cobalts, so win win there

C) Illums can muscle their way through flak. Flak can sorta win that battle, but if only has some, illums will muscle through that too.

D) I think you're being outproduced, meaning either you're not getting enough planets early or you're spending your money where you shouldn't be. That's a guess

Just to confirm - he is out producing you because he is building more/better ships right? Not because you can't build anymore as you have run out of fleet supply?

definately do not buy upgrades many updgrades on weapons, especially online!  start your battleball, i.e. illums, flak, aerias, mothership, halcyon, and rapture, adn just few guardians.  play this startegy right, and you'll almost never loose more than a few ships each large encounter, if any.

You should only build enough disciples (maybe 1 or 2 though even this you might not need) to help with clearing planet militia before you can get illums pumping out. Put three weapons labs on your homeworld, you will need to upgrade logistics, and then start teching illums asap. If playing quickstart on a relatively small map its a good idea to scuttle your cap ship factory. 

After that point it depends what the enemy is doing. You should make sure you are scouting effectively in the early game, e.g. know what is in your opponents fleet and where it is/how big it is. If you think they are going to rush you should tech repair platforms and put some where he is likely to attack. If you do not think he is going to rush you I would usually start teching up to defense vessels and guardians. Defense vessels tear up enemy fighters which would otherwise counter your illuminators. If he has gone for early trade ports its likely his fleet has had to suffer so you may consider rushing if this is the case. Repulse is an important tech to get - it can neutralise enemy flak and heavy cruisers (e.g. kodiaks) not to mention cobalts (though illums tear these up anyway). You can use it to separate his fleet allowing you to take on a small portion at a time.

Generally its worth it to get the tier 1 hull upgrades too - they are cheap for what you get. Also consider getting culture up once you have 5-6 planets if you have the breathing space to do so. Culture increases your allegiance thus increasing your economy, and can force the enemy to get his culture up early (advent get the access to culture cheaply and early compared to other races). Weapon upgrades shouldn't be rushed to, particularly for illuminators (expensive!) I tend to get them once I have maxed out fleet supply (after a couple of fleet supply upgrades) and feel that my fleet is a respectable size compared to the enemy's.