The ancients provide bonuses to the game in a way that is preserved through ascensions. This comes in handy in the game and for now could be considered the end-game gameplay as those are what you are trying to acquire and then level up to increase your capabilities. You can find a list of all their capabilities on the Clicker Heroes' Wiki.
To answer the best time to summon I will kind of echo what @Chippies has said in that there really is not a best time to do it. This game is Very dependent upon your DPS. This becomes more apparent as you go through more ascensions and accumulate Hero Souls. These souls on their own provide a 10% increase to your DPS. It is also the 'currency' that you use to summon and level your ancients.
To that end, as I found out last night first hand, summoning Ancients early on in your game (and by early on I mean less than 10 ascensions) can really slow down your progress unless you get very lucky on your ancient selection. 40% DPS is hard to beat with the abilities of any of the ancients. That said however there are going to be play styles where it will make sense.
An example of this is if you keep the client live in a browser tab or close it down most of the time and just check in. The two ancients that @Chippies mentioned, Libertas and Siyaltas both increase your gains Only when you are not actively playing the game. If you are doing long stretches of time between clicking sessions and are given access to these ancients then they can indeed be of use. The cost of rerolls to find them however have a good chance of keeping them out of reach.
My suggestion overall. Use the save feature. Save your game, keep it safe and get an ancient. See how it affects your game play. This is what I did last night, I dropped about 15 souls into Vaagur to almost cap out his level. It dropped my DPS by so much that even though I could use the skills every 2.5m or 5m or 15m depending on which they were that it was useless to me.
Do not be afraid of trying things out and resetting if what you see is not what you were expecting.
When you ascend, you'll receive 1 hero soul per 2000 hero levels. (unless changed)
Basically if you have a total of 5310, you'd get 2 hero souls.
Before you'd get cooldown reductions, damage, more gold and so on. But now I believe that you only get a % of damage. (you can read if you hover over the hero souls text)
If I'm correct, it's 10% extra DPS per hero soul that you have.
I think I did my first ascension around level 100, but like I said, you had more/better extra stuff by then.
I'd say do an ascension whenever you feel that you are ready, then try to get as far as you can, without spending ages on each level, then repeat.
It's hard to say when the best level for ascension is but yer, I lost my savefile and I got pretty damn far. :3
Best of luck to you.
Best Answer
The regilding is immediate. No fight needed.
You pay your two hero souls for the regilding, then you immediately get the screen like you just gor a new gilding and you have to click to open a chest to discover your new gilded hero.