A very good question, I was actually planning to post a very similar question on the very same subject, but it would seem you beat me to it.
After all, just like yourself, I have never played any of the previous Stardock games and am a complete and utterly unfamiliar face when it comes to this company and their previous releases, having only learned about Elemental through word of mouth and rumors.

While I do want to know the answer to this though, I fear it might be wrong to ask the beta-testers about this. The main reason for this is that many of them, if not the vast majority, or avid and seasoned veterans from previous Stardock games, just like Sins of a Solar Empire or GalCiv2. Asking them, veterans of the 4X genre, whetever the learning curve is smooth or rigid may be a bit redundant, as their opinions would not be that of a rookie-player who have never touched a game like this before. Granted, I'm not saying that the beta-testers opinions don't matter or wouldn't carry any weight, on the contrary, they should be very familiar with the UI and interface of the game by now. Still, if anything, it would likely be best if a person, similar to you (the OP) and me, who are not that familiar with previous SD titles and the 4X genre itself, to respond and answer this querry.

From my understanding, the single player campaign will function as a tutorial of sorts, though it won't be in your basic tutorial format of a voice over telling you exactly what to click on. It should introduce the relevant concepts and controls, though.

Otherwise, it's not actually that easy to say. The beta was pretty unfinished, including unpolished and confusing UI in many places which obviously makes things harder.

To be honest, in your position I would wait for a demo, which will come sometime after release. You may have to wait a few weeks, depending on whether or not SD has time to relax and make a demo build or scramble to fix serious issues (hopefully not!). Some reviews, especially video reviews so you can see how it plays, should help as well - but the demo will be tough to beat.

Not to put you off, but as far as I understood Elemental will be for the experienced 4x crowd in the first place. No, I don't know it first hand and it may be approachable at the same time, but everything Brad indicated the last couple of days clearly hints in that direction. He said that there will be no Tutorial per se and that the campaign plus an ingame "encyclopedia" will be the only means of explaining game mechanics. Also, in the latest interview with FiringSquad he clearly stated that Elemental's focus is on the hardcore audience.

http://firingsquad.com/games/elemental_war_of_magic_interview/page4.asp

FiringSquad: Have there been difficulties in balancing deep, complex mechanics with ease of play? Are you trying to appease the hardcore micro-managers or cater to the more casual crowd? 

Brad Wardell: We’re catering a little bit more to the hardcore than your typical game. In fact, we’ve actually said we’re probably going to get bitten on reviews because this is a game that is designed a little bit more… We’ve had 5 or 6 years of every game coming out saying “Well, we’re like the old game that everyone loved, but we decided to simplify it to make it more approachable.” That seems to be the word of our new era in game design; we want everything to be “approachable.” Well, I don’t want Elemental to be that approachable. *laughs*

I want to be able to equip my units with weapons where there’s a difference between a cutting weapon and a piercing weapon, and have some subtleties in that. We are putting in a lot of work to make sure the userinterface and the information is there, but we do want to… Let me give you an example. Tactical battles, right? How do you make a mounted warrior more effective than a footman, but not have it be a rock-paper-scissors [situation]. We do that through action points – there’s a system for handling how action points are done based on what equipment your unit has.

Some might say “Well, that makes the game very unapproachable to someone who just wants to go into battle and kill stuff.” And my answer is yeah, it does. So, it’s one of those choices where, if someone wants a really casualized strategy game, there are plenty of options out there for that. On the other hand, there are some really in-depth strategy games out there, and we’re not quite to that level, but it’s definitely not a casual game.

So as much as I want to give you an immediate recommendation to buy it, I have to agree with the suggestion to wait for the demo.

Rip - Never fear there is one key difference between Elemental and Sins.  Elemental is Turn-Based.  You can take all the time you like analyzing the situation, reading the built in help system, etc.  The pacing of this style of game helps new players.  Also, there will be lower difficulty levels were you "the player" have an advantage over the AI.  This will help compensate for strategic mistakes while you learn the game and hopefully make it feel "fun" right from the start.

Look at it this way.  Isn't it nice that you have this concern.  It means this game isn't the same 'ole same 'ole.  There is something to discover.  New questions to tease your brain. 

To address your second question  - the UI pictured in recent screenshots provides more visual clues that something needs your attention than games in the past.  This should help you identify what to do without digging through menus or dealing with popup boxes like so many other 4x games use.

Finally, you can always come back to the forum and ask questions.  Overall this is a better than average gaming community.

I think one of the beautiful aspects of Elemental is that it has a lot of detail and thinking man's stuff in it, but you can also avoid it if you want. Like you can design your units down to the equipment if you like micromanaging your armies. However, there are pre-built generic units too. They did a pretty good at abstracting things out enough that it's not as complicated as strategy games of the past. You also won't be building a bunch of cookie cutter towns due to the way resources work. Once you get the basics down it can be as deep or as quick and dry cut as you want it to be. They don't dumb things down, but they don't force everything on you. Elemental might overwhelm you if you force yourself to go through every little detail, but I think it's one of the least overwhelming TBS game I've ever played. The most complicated thing you might have to keep track of is what resources are near what town, and what to lock down. You can spend most of the game just adventuring with your sovereign though.

I'm just saying all of this based on the beta, and what Brad has talked about in recent interviews.

I too would wait for the demo if I were you based on the fact you said you find the Civ games hard to get into and understand.  And Elemental in my opinion is more complicated then the Civ series.  I personally was getting the gist of Elemental within a few minutes but then again I've been playing turn based games like Civ for nearly 20 yrs so you might consider me a vet of turn based games. 

Sins gave me some fits because RTS is not my favorite thing but after a couple hours I figured it out and Sins is still a great play for me from time to time.

Wait for the demo.

I think Elemental is much more complicated then Sins. On the other side it is turn based and you can take your time to learn it without being crushed after 5 minutes (that being the drawback of realtime games).