The "lost cards on upgrade" is an illusion. (Well, poor interface design, to be percise.)
The upgrade animation shows draining of all cards, but the extra cards are actually saved. If you have enought cards, you can even upgrade a card multiple times in a row.
You should feel free to upgrade your cards without a worry. (Other than spending too much gold.)
As you can see here, the gold contens of a chest very much depends on the arena you currently participate in. You say it is Arena 3 (Barbarian Bowl), so that's what I am assuming throughout the reset of the answer. Higher arena means more gold, so faster gold-getting!
A silver chest will give you (averaged) 38 gold, and a gold chest 127 gold. I disregard the giant and magic chest, see that as a bonus if it pops up :). There are 180 silver and 54 gold chests throughout the whole cycle (source), so roughly 3 silver chests per 1 golden chest. If you open them in order (that is, SSSG), you'll be netted (38*3 + 127) = 241 gold in 17 hours (3*3 + 8).
However, there are also free chests and the crown chests, that add to this amount. You'll get roughly 4 free chests in this time period, and 2/3 of a crown chest. I'm not sure how much this is, feel free to comment this if you are on arena 3 and open a free/crown chest, I'll add it in. This depends on your playstyle: if you play only a few games per day, not enough to win the crown chests, it takes longer. If you play just once a day, you can only open 2 free chests, instead of the theoretical maximum of 6.
Furthermore, you can donate cards in your clan and get money (and experience) in return. How much you donate is completely up to you. As told here, it is a maximum of 4200 gold per week. You'll get 5 gold for a common donations and a staggering 50 gold for a rare donation.
In conclusion, it differs quite much per player. If I can get the gold per crown/free chest, I will calculate the approximated time when you play at maximum efficiency.
Best Answer
The donation system now works this way:
Every 7 hours, the members of a clan can ask for cards (common and rare during the week, epic during Sunday). Depending on your arena level, the number of cards you can give/receive is modified. If you donated too many cards during this 7 hour period, you will then have the cool down, preventing you from asking/giving further cards.
The number of cards you can ask/give for each arena is the following:
Goblin Stadium
Bone Pit
Barbarian Bowl
P.E.K.K.A's Playhouse
Spell Valley
Builder's Workshop
Royal Arena
Frozen Peak
Jungle Arena
Hog Mountain
Legendary Arena