DISCLAIMER: Every hint you can find below is based on my experience and shows my own opinion. Other players might not agree with me at every single point here so feel free to look for other opinions.

hintid1 Golden or Silver Chests? Which should you buy for gems?
Answer would depend on your targets. For simple comparison:
  • Silver chests
    • You get more gear pieces per gems spent - at least 10 vs max 3 from golden chest per 500gems.
      This means, that as long as you don't have just any item in every available slot - choose silver chests.
    • You get approximately 50% item levels per gem spent.
    • You will always get some gold from those chests, which you might use to upgrade your champions a bit and push further.
      With this knowledge, you should keep them in your inventory till the point, when you're unable to push further and use them to progress a bit, which would result in more favor gained.
    • Overal higher chance to get shiny item per gem spent. While actual probability to win shiny item from any chest is the same (around 0.1%), with silver chests you're testing your luck 10 times vs single chance in golden chest per 500 gems. Remember though, that 10 chests won't give you 1% chance, just like 1000 chests won't give you 100% shiny. It's just more dice rolls and natural 20 is still far more probable.
  • Golden chests
    • Only source of Epic equipment. This means that if you are targetting to get "full purple", you have to focus on golden chests.
    • You have 100% chance of getting at least Rare item. This is a huge boost over either Common and Uncommon, so after you get every slot geared with either of those from silver chests, your best bet is to open those, to get both Rare and Epic equipment in process.
    • Only source of Epic (Huge/Large) consumables, i.e. contracts and potions. If you want to maximize buff you're getting from using potions, you will need items of every kind of rarity.
    • Only source of bounty contracts. Not just Epic, only source for any kind of bounty contract. While both bounty contracts and silver chests drop gold, only contracts drop event tokens during events.
Some statistical info, quoted from steam store product page:
  • Chance of a Rare equipment card in a Silver Chest is approximately 3.2%.
  • Chance of a Rare equipment card in a Gold Chest is 100%.
    Chance of an Epic equipment card in a Gold Chest is approximately 12%.
    To mitigate bad luck, a system exists to guarantee at least one Epic equipment card within every 10 Gold Chests.
  • Chance of a Shiny equipment card in a Silver or Gold Chest is approximately 0.1% per chest.
To sum it up, if you are focusing on getting gear only (leaving gold and consumables behind), first focus on silver chests to get an item for every slot. Then, switch to golden chests to get at least full Rare (obviously with some Epics). When that is done, you can keep going for golden chests until you will see only purple equipment slots or go 50:50, or whatever rings your bell. After you get to full Epic status - go for silver chests only (remember, that's if you only care about equipment levels on core champs). Both kinds of chests offer you Blacksmith Contracts as well, to help you increase item levels further, but there is not much of a difference in how many levels you will get through contracts from either kind of chest. Value of contracts gained per gem spent should be about the same.
hintid2 Which DLC should you buy?
You SHOULD start with these two: After those, if you're really sure that you want to spend money - buy familiars. There's never enough. Why not Champion DLCs? You will easily gear them up without those DLCs. It will make your grind a bit longer, but if you will really play this game to complete it in 100% then you have at least a year of playing as more and more content is being released. No need to be in a hurry.
If you wonder if Founder's Pack DLC is worth it - it is (has familiar in it), but it's expensive and offers an interesting weeklong buff, that you won't be able to fully utilise as a new player.
with your support it will be ready in about 6 months or ... sooner