I have been a bit apprehensive about opening the game up on steam initially, as I have seen people's forum posts about their profile not carried over and that it got written over with a brand new account.
(Please do contact the devs if it happens)

I managed to got it synced/linked up.
First when you boot up the steam version of this game you would go through a bit of initial loading up (Pretty much similar to after a version update for mobile players).
Then you would see this:

Don't create a new character, login to your existing Eternium account.
After syncing for a bit, it will load up your character screen like you are used to in the mobile's format.

So first we would start off with a character and get into gameplay along with the initial tutorial.

At this point, most would notice some monetisation stuff, but it is ok. Gems are relatively easy to get, perhaps it doesn't seem so right at the start though.

This first character you created would be expensive to max out (Inventory size, skill usage slots).
What you would want to look into long term is the shared stuff:
Things like your crafting level,
Shared treasure chest warehouse,
Recipes bought from the recipe shop with coins over time
Character slots up to 5.

Personally I would wait for ANBs to start. (https://forum.makingfun.com/forum/eternium/guides-and-walkthroughs/167521-anb-event-planning)
ANB= A New Beginning event

The characters in ANB would fill up your 5 slots eventually, with one created each ANB.
During the ANB event itself:
Your ANB character is not counted towards the 5 slots,
Stuff aren't really shared except for gems and crafting level/crafting related recipes,
There would usually be gem drop boost through the event.
ANB characters get a reduced pricing in terms of gems for unlocking skill usage slots, companion slots and inventory space expansion.

Seeing this, especially the last point, Characters that you play and want to keep would probably come from such events, since it is easier to max them out.

Eventually there would come a point you hit lvl 70 along the way. Have at least one lvl 70 character in your account to farm for some lvl 70 items for that class (There are more complicated things regarding very good item drops, can find it in : https://forum.makingfun.com/forum/eternium/guides-and-walkthroughs/149389-eternium-walkthrough) and to get exp towards Champion levels, which will apply through all the other characters in the 5 slots.

Rough summary:
Don't get too attached to your first character, it is a pain to max it out.
Conserve resources, spend gems on ANB character that you want to keep for general gameplay.
There are Champion levels that apply stats modification to all characters. (Earned by lvl 70 characters getting exp)
Your crafting lvl is shared, during ANB you get a reduced cost to make items (Though you can't keep them usually) so use it to get craft exp.
Deleting character costs gems. For your first 3 to 4 ANBs, be sure to make characters in classes that you want for keeping in usual gameplay, unlock their every skill usage slot, inventory spaces and companion slots.
After filling 5 character slots, the ANB event character will delete itself once you click and confirm on ending the event when time runs out. Their items and exp will get merged with the main account (Items in mail, exp to champion exp level usually)
So hmm in that sense no need to spend 50 gems to delete characters after all character slots are filled.

Thanks if you read to this point of my rambling :D

Try not to buy the Golden Treasure chests you find in storyline maps. They usually don't have the best items and unless you really are lacking in whatever it is inside them at that point in gameplay, usually I would keep my gems and stock up.