Is this how it usually goes?

I'm just starting out with Bitcoin and trying to get a grip on how everything works. I've been reading about transactions, nodes, and private keys. I thought it usually takes 10 confirmations for a transaction to be fully processed, but when I sent some Bitcoin to another wallet, it only took about 5 or 6 confirmations to show up. Is that typical? Does the number of confirmations change based on the transaction size? Also, I'm curious about how the Bitcoin network decides the order of transactions in a block. It seems pretty complicated to me. If I got any of this wrong, feel free to correct me.

You supposed to see the coin after 1 confirmation. If you you are using exchanges, they can increase the number of confirmation but most exchanges now have 1 confirmation for deposits while 2, 3 or more confirmations for withdrawals. But if it is bitcoin network and not a centralized service, it is 1 confirmation.

That is normal but also a lot of transactions initially show up as "pending" or "unconfirmed" and you should not consider those final.. The gold standard has typically been 6-10 confirmations as it's not too long to wait but generally after 1 confirmation it's unlikely the coins can be reversed and after 2 it's virtually impossible.

Technically a block is considered fully confirmed after 101 confirmations. That said, when someone considers a block safely confirmed is entirely up to them and some will accept just 1 conf. As others have said, it is a matter of how difficult it becomes to undo a tx: The more confirmations a block (and the txs' in it) has, the further back the chain would have to be rolled back to undo the txs'. Anything past 5 confirmations would be virtually impossible to roll back. In reality the only time it really matters is during orphan races where the winning block may or may not have your specific tx in it. These days, most businesses and exchanges are satisfied once a tx has 3-5 confirmations.

Which wallet do you use? I'd say the choice of wallet is much more important than waiting for more than 1 or 2 confirmations.

Regardless of what your wallet says, if you send bitcoin to a merchant or company, they will consider the transaction confirmed depending on the amount. If you send, say, $50, it is normal for them to consider it confirmed after 1 confirmation because it is extremely unlikely that anyone would even think of creating an alternative chain to scam you out of $50. For larger amounts, it may take three confirmations, or if you send $50M, they may want to wait for six confirmations. So, when it is confirmed is a bit relative. But this is pure theory IMO. In practice, I don't think there has ever been a scam, or the creation of an alternative chain to void a confirmed transaction after 1 confirmation. So, the 100 confirmations seem too conservative to me, considering that the difficulty grows exponentially with each confirmation.

101 confirmation is the number of confirmation needed for a Coinbase reward to be "matured" so that it can be spent which is I believe the reason why @NotFuzzyWarm says a block is "technically confirmed" after 101 confirmations. It's an overkill for regular use cases under normal network conditions (3 confirmation is more than enough). The purpose of 101 confirmation for Coinbase reward is to prevent a "mess" in case a reorg happens and it needs to be a fixed value that is also big because you can't change the rules based on network conditions dynamically. But for regular use cases as individuals (or services, etc.) you can set any number dynamically. You see the number of confirmation required to consider a transaction irreversible is not a fixed thing. It depends on a couple of factors. For example the size of what you are receiving, the person that is paying you, the client type you are using (it is safer to trust your full node than your SPV client), and most important of all the network conditions. Normally, there is nothing going on. The miners are all mining on the same chain building on top of each new block that is created and worse case scenario we may end up seeing a single block re-written. Which means accepting transactions with 1 to 3 confirmation is safe. But there are times when the risk of chain-split is higher, like during forks or maybe some day a hashrate attack. For example during the mess back in 2017 it was safer to wait for more confirmation than usual (the suggested 30) due to higher risk of a chain-split.

Times of chain-split barely happen but your example on what happened in 2017 chain-split and recommended confirmations (30) is very good example. In other normal times without chain-split, there are recommendations on how many confirmations are enough. People can use calculators for understanding more about risk of 51% attacks and also take a look at confirmations recommended that are based on value of a Bitcoin transaction. How Many Bitcoin Confirmations is Enough?

I have gone through all replies and now understand it better. Thank you all for helping me understand.

Merit given for acknowledging the help folks have given. That is far too rare here.