you had a number of questions. Ultimately there is no definitive right or wrong answer when it comes to tone, you either like it or you don't, but I have been playing for about 25 years & used to trade guitars, amps, etc, so I can pass on some of what I have learn't (i won't call it advice) & you might want to consider it in this order.
Effects - if you are going to use effects a lot, all you need is a clean amp - let your effects do the work. if you want best bang for your buck look at a Zoom multi effects unit as they have pretty much everything in one package, you can fiddle with it, figure out what you like best & invest in higher end stomp boxes when you know what you want. They also model amp sounds, which will give you various famous amps sounds as well. BTW the "two Guitars" sound you are hearing can be replicated using an Ocatve effect (zoom has one of these in their multi too).
Guitar - I have assumed that your guitar feel, etc is ok, but with a strat you are playing with three single coils, just like Yngwie appears to be, but he is given guitars & technology that is simply not accessible to you on a budget (i.e. fully scalloped neck). One of your real issues here is the output of a single coil strat pickup. To play the type of music you are listening to & to get the output you need, have a look at a single coil (size) bridge humbucking pick up or Rail. this will boost your output instantly & significantly, improving sustain also. you may need to get someone to install it, but as it is single coil size you wont have to replace pickguards, etc & there are plenty of really good quality units out there that are not big brand names & marketing budgets, that do a great job.
Amp & speakers - bigger does not necessarily make better. If you are after tone & using a lot of effects just look at a speaker upgrade. Do a youtube search "celestion vs" and there are pages of comparisons. Warehouse Guitar Speakers have some really good products for the money & significantly out perform the chinese made celestions, but check out what Yngwie uses in a gear review & choose a speaker that is relevant for the sound you are after.
If you want an idea of what guitarists will do to get "their" sound, check out Vernon Reeds Rig review on youtube - mind blowing! his base 2x150Watt Mesa boogie amp heads played in stereo...I saw him play live with living colour & I have never heard a guitar sound like it before, amazing! But Remember, these pro's are awesome guitarists even if they just plugged their guitars straight into an amp, no effects. Regardless of all the tricks & tech, nothing beats hard work, time, dedication & progression, so keep at it.
I hope this helps a bit.
