I invested 800 gems for masteries for my Kael which was my first 60.  It really helped me in maximizing my training for 12-3 or 12-6 and the Clan Bosses.  

If you plan on playing the game long term, you want to maximize your Market slots and maximize the Mine.

You shouldn't use gems for expanding your Champion slots.

Don't buy ancient shards until there is an event which gives you bonus for them.

No! Buy every ancient shard you see - and save them up for the event. There is no need to open a shard immediately after buying it. Shards are one of the very few things in this game that have no storage limit.

I think he meant don't spend gems on shards, do buy them for silver in the market. That would be my recommendation as well.

gem mine is useless, you get very few gems in a single day. in fact the gem mine is one of the most annoying things in this game. you will literally have to spend a whole day and you will still not have enough gems for an energy refill

And  XP  boosts.  I  always  buy  them  whenever  i  dont  have  them  with  a  lot  of  energy  or  during  a  champion  training  event  or  tournament.

Amd  gem  mine  isnt  useless,  it  is  the  best  possible  thing  to  spend  gems  on.  It  pays  itself  back  in  100  days.  It  is  a  reliable  source  of  gems  for  a  F2P  player.  It can  quickly  build  up  into  a  stockpile  if  you  dont  just  buy  refills  on  random  days.