Most of what I'm about to say has been said previously in this thread, but it bears repeating.
Beginner Collection BuildingYou need to start by going in with a plan. Pick a commander you would like to build, build the deck on a site like Deckstats, and then plan out what you want to buy.
Assassin's Trophy is very good removal but you might not want to shell out that much money. You have to be careful with spending a lot of money early on, because you don't want to buy cards that you'll likely never use or never trade away. Buying a commander pre-constructed deck is a good way to get your foot in the door without breaking the bank.
During this stage you'll also want to keep an eye out for good cards that can go in multiple decks. That way, when you get tired of a deck and take it apart, the cards will be transferable to another deck. These cards are often called "staples". Here are some staples that aren't too expensive and will go in many decks throughout your commander career:
Using EDHREC is a good way of knowing what the most played cards are, but just because they're popular doesn't mean you'll always use them. Some cards are overrated. Figuring out what cards are staples will just take time as you play the game more.
If you're looking for the most cost efficient way to build up a collection
do not buy booster packs. It is very rare that you'll consitently get your money's worth by buying packs (some sets like Modern Horizons 2, are the exception). Buying singles ensures that you're getting exactly what you want instead of gambling and it supports the game store more than buying sealed product.
Advanced Collection BuildingOnce you have a number of cards you're going to want to make a trade binder. Never let this thing out of your sight; theft from trade binders is very common. I'm extra paranoid about this stuff so I just send people the link to my collection on Deckstats and let them pick out the cards from there.
When making trades, people will often try to match the prices of the two trades so no one is getting ripped off. The MTG Familiar phone app is good for this. If the cards you want are $15 and the cards your giving are worth $15, it's a fair trade... usually.
There comes a problem when there is a gap between the two trades. Let's say that you're offering $49 worth if cards and the person you're trading with only has $40 worth if cards that you want. Then you can do a "value trade" when you
browse through their trades looking for another $9 worth if cards. Be careful here. Just because
Thada Adel, Acquisitor is $9 doesn't mean that you'll ever use her in a deck, or that you'll be able to trade her off.
When I need to value trade, I go for cards that I know I'll be able to trade at a later date. There will practically always be a demand for cards like
Birds of Paradise and
Arcane Signet. In the before-times I would often trade for
Smothering Tithe, and now look how much it's gone up in price. Knowing which cards are good to trade for will take experience, which is why I didn't include trading in the beginner section.
Generally though, trading exclusively for cards that you want for a deck is better than value trading.