i'm with the original core, if you talk about desktop, for mobile i like "bitcoin wallet" very akin to core, i don't like spv client, those light client

for web greenaddress and circle are good, or xapo

I use online XAPO wallet for every day transactions. I find it quite good and also no fee on any transactions.

It depends for what you are using it and how many coins you will store. If you have considerable amount of money in BTC, consider Trezor or if you don't want to invest into a hardware wallet then use paper wallets.

Mycelium is a great, great wallet for Android. For your PC, I suggest Electrum or even Multibit if you don't want to run the core and download 40GB of the Blockchain.

I would stay away from the online wallets, with them you are not a solely owner of your private keys.

Good luck!

I use coinbase since more than two years. It is used by millions of people and one of the most (if not the most) usable web wallet. Have one specific that is offered only by this wallet. The fee that you must pay when send bitcoin from your wallet to another wallet are paid by coinbase if you are a coinbase user.

I use electrum and recommend newbies to use it. With electrum i don't have to download whole blockchain which is about 40gb in size.

I use Coinbase

It has a good foundation and backing so I see good in that.

Plus, they've been adding more and more features which I enjoy. 

Coinbase pay the transaction fees for you? I didn't know that. That is great for newbies when they collect dust from faucets and giveaways. I might register for one, thanks.

Apart from the fees, I think light wallets like Electrum is a good start for newbies. No need to download the 40G blockchain and easy to restore.

I think it is more best type of wallet not a single wallet.  And that type is cold storage.  It can be as simple as a paper wallet if done right.  But again you have to do it right for it to be secure.

For those unsure of doing this I would recommend a good hardware wallet.   That is my second best type (possibly first if price was not there).   

i Recom electrum
reason:
- SPV client. do not need to download all blockchain database.
- Hierarchical Deterministic wallet. Always replace each received bitcoin address.
- Backup is easy. Use secret words that can be recorded on paper.
- Support Multisignature P2SH.
- Support Two Factor Authentication.
- Support Hardware wallet.

Full blown bitcoin-core wallet is the way you'll wanna go if your planning long-term bitcoin involvement.

An SPV wallet of some sort (i.e. MyCelium) might be what your looking for if your more of a short term I need it now kinda fella.