I have C-Boldtusk, G Falcon, or Sun-Shangxiang for reds and C-Melendor, Hansel, C-Caedmon, or Kashrek for greens…who should I ascend? For context, I’m just beginning to ascend 4*s and have ascended three so far - C-Kiril, Wu Kong, & Merlin.
Priority of course for long term use, otherwise trying to keep boosting my Titan scores as those have been my best bet to getting more gloves which is what I lack for ascension mats right now
Great choices for red!
I’d do them in that order. C Boldtusk - Falcon - Sun-Shangxiang
For green I would do - C Melendor - C Caedmon - Hansel and I’d hold off on Kashrek
Cheers!
Regular Boldtusk (with costume bonus, and later +20 with limit break) will serve you well for many years
Boldtusk and Caedmon first. They were two of my first.
Boldtusk is great and even with a good 5* red bench he still sees action, his stats are great with emblems and limit broken.
I really like Hansels mana control, used him a ton back in the day although his stats are probably a little dated compared to costumed heros. For immediate use id go hansel but for longevity c caedmon or mel
In the long run you definitely want to have at least 1 good 4 star healer on each colour, but healers alone are not going to get you anywhere in this game. So I would maybe do 1 healer, 1 non-healer for now.
I find Boldtusk the better of the 2 healers, but so are your other red choices better than the greens. You´ll definitely want to get all 3 reds, but the Falcon needs other red hitters to benefit from his def down, so don´t upgrade him first. Sun is awesome (one of the best def-downers in the game).
Among the greens I think Hansel might be best. He´s kind of the green version of Merlin, faster, but only stealing half the mana. If you like Merlin, you´ll like him, too. They can work as a tag team, too 
CCaedmon is also a good option with the possibility to either dispel or cleanse. If you want dispel you can use Melendor though, he´s better suited to dispel counterattacks as he doesn´t have to hit first.
Kashhrek is a good tank early on, if you like him get him right away, he will be losing usefulness faster than all the other options.
So I would maybe go with Boldtusk/Hansel or Melendor/Sun.
All the 3 reds will give long time use and in all likely hood all 3 for the rest of time 
Sun is the red with the highest def down.
Unless you get extremely lucky and pull C.Marjana, Falcon will be your red down for ever.
And I agree with Boldtusk also being one you will continue to use.
When you say ascend and not level I assume you have all 3 at 3.60? I don’t know which level titans you are facing but assuming you can stay alive and for green titas you use all 3 red + wu I would ascend Sun first. She has the highest attack stat of these and getting that up would help you with titan hits.