These are your options in order from best to worst:

Solid State Drive (SSD)

A solid state drive will provide much faster access than a mechanical hard drive. Amazon shows that in August 2015 you can get 250GB external SSD for around $150. According to Game Debate Fallout 4 requires 28GB of hard drive space so you could target an even smaller drive to reduce costs. You may also choose to assemble your own drive by purchasing an internal SSD and a 2.5 inch USB 3 Enclosure to contain the drive. The enclosure should be able to be found for around $10.

You should be able to assemble a 120GB drive for under $70 and a 60GB drive for around $50 from either Amazon or your local computer parts store. My examples above are assuming you are in the USA, but as another example here in Australia I could assemble a 120GB SSD in a USB 3 enclosure for under $90 AUD.

Powered 3.5 Inch Mechanical Drive

A powered external drive will be larger than a portable drive (and not very useful if you are on the go) but it will provide ample space (multiple terabytes) and should perform similar to a mechanical hard drive that you would have found inside a desktop PC a few years ago. Note that these days most "gaming" PCs will be built with Solid State Drives internally.

"Pocket" 2.5 Inch Mechanical Drive

A pocket drive is still usable, and can be found quite readily and cheaply. Be prepared for long loading times and transitions, and also long install times when using Steam as it will have to pause during downloading to wait for all the files to be unpacked to the disk. I had significant success using one of these drives a few years ago to play games under Boot Camp on a MacBook Pro, allowing me to install lots of games but keep a small (20GB) Boot Camp partition.

Flash Drives / Memory Cards

Even though flash drives have no moving parts like an SSD, there is still a large performance difference between the two types of drives, especially when reading or writing multiple files at the same time. The performance can be improved by purchasing a high quality (and expensive) memory stick, but at that stage you would be far better off getting a 120 or 240GB SSD.

Realistically, the speed of the drive won't affect gameplay much. The main benefit to a HDD would be capacity and price, as an external SSD will not run nearly at the speed the price would imply when connected via USB 3.0. I gamed for quite a while on a USB 2 external HDD, and I never experienced any major issues, save for slightly extended load times.

If you ruled out an SSD due to price, it's very unlikely that you will get a flash drive with adequate performance. There are fast flash drives, yes. But I never saw a really fast flash drive significantly cheaper than a SSD (per GiB).

Also: Flash Drives don't support the TRIM command, so they will get slower over time and there is not much one can do (depending on controller: total wipe and write zeroes). Your use case will delete and write much more than the typical flash drive usage of puting some files there and reading them back, irregularly. So after some time (depending on the amount written during your usage and the free space left on the device) every part of the flash will be used, and there is no way to tell the drive that something is not needed any more. This means on every write the drive has to erase the flash before and copy some data. Performance will be quite bad then.

If you buy a HDD, you should buy a external case with a fan or at least made of aluminium, to spread the heat from the drive.

An SSD or flash drive is not significantly faster for gaming than a traditional hard drive because game assets are packed into big files in the right order for sequential access, negating the SSD's major advantage.

The answer then is "it doesn't matter", whichever is convenient to you.

I'll start off by recognizing that the OP said they were not concerned about price, but then in a comment said they ruled out using an SSD because of price. I think the OP has mistakenly assumed that a spinning disk or flash drive will be cheaper than an equivalently or better performing SSD.

They're wrong, especially given they only need about 64 or 128G, an SSD is the fastest and most economical option. I'm interpreting the OP's need as "I need an external drive for gaming on a tight budget".

The tl;dr version is that spinning disk performance isn't in the same league as flash drives and SSDs. A fast flash drive in the size you need will cost you $140. Instead, for $60 you can buy a cheap SSD that will perform as well as that flash drive, for example the Kingston SSDNow or the OCZ Trion 100. For $75 you can buy an excellent SSD such as the Samsung 850 EVO.

Here's the details.

There's a lot of very cheap, but very slow external drives out there. It's hard to know what's actually inside the enclosure, external drives rarely provide performance information. Let's ignore them and instead focus on putting a bare hard drive into an enclosure.

A decently fast spinning drive will cost you at least $50, for example a Seagate Barracuda, plus another $20 for an enclosure. If price is no object, there is the WD VelociRaptor 600GB, one of the fastest mainstream spinning disk drives, but it's going to cost you $250 and it's going to suck power like nobody's business. You can get a 300GB refurb for about $60. At a max transfer rate of 145Mb/s it's only 1.5 to 2 times faster than the much cheaper Seagate Barracuda. You're just not going to get huge performance gaps with a mature technology like spinning disk drives.

What about a hybrid drive, a spinning disk with a small SSD for cache? In 2012, when SSDs were expensive, they made sense as an economic compromise. In 2015, when SSDs are affordable, they're dead tech. They're only useful when you need a lot of fast disk space on a budget. You can pick one up for about $80. While it will outperform the Velociraptor for small, repetitive, easily cached transfers (usually having to do with the operating system) which will be using the SSD, large or infrequently used files (such as loading a new level) will not do well.

Flash drive performance varies wildly. And you're going to want at least 64 GB to be safe (as a comparison, Battlefield 4 wants 30 GB) which jacks up the price. A fast flash drive of that size is going to be anywhere from $50 to $200 depending on how fast and how big. A Corsair Flash Voyager GTX 128G is a good choice. At $140, it can read three times faster than the Velociraptor.

Here's the "money is no option" lineup from slowest to fastest.

• Any hybrid drive
• WD VelociRaptor at $60 to $250 for about 140MB/s
• Corsair Flash Voyager GTX at $140 for about 450MB/s

Ok, what about an SSD? The OP ruled them out because of price, but there's a number of well performing SSDs for $60. The Kingston SSDNow or the OCZ Trion 100 will both perform better than the Flash Voyager GTX, especially at random reads and writes, at half the price. Bump up to $75-$100 and you can get the amazingly well balanced Samsung 850 EVO.

This is all moot because with a brand new, graphics intensive FPS game like Fallout 4 your bottleneck will likely be your video card. The OP said they have a MacBook Pro Retina Mid 2012 which means, fortunately, a dedicated GeForce GT 650M. This should be better than the minimum requirements. I'm making that assumption based on Battlefield 4 and Arma 3 having a minimum of the inferior GeForce 8800GT. But it's not great.

Before you go spending money on hardware for a game that doesn't exist yet and we don't even know the system requirements, try running a game like Battlefield 4 or Arma 3 and see how that goes.

Why don't you use BOTH.

Introducing the Hybrid Drive! *

You don't really see much in the press about HHDDs these days, and the only company that does them is Seagate, this is because in the majority of cases, users find SSDs to be cheap enough. However there continues to be a small niche in users who want to have fast random access in their humungous storage solutions, the Seagate HHDDs are pretty good.

However I would NOT connect a hybrid drive to a PC using USB3 if at all possible. You would get much better performance by attaching it via a eSATA connector. If your Mac lacks an eSATA connector, I would advise you to fork out for a Thunderbolt-eSATA connector.

*No I don't mean attach a Prius to your laptop.