With any computer (be that a desktop one, a laptop, a tablet or anything else) you need to consider the size of the hard drive (or solid state drive, which does the same thing) and how much 'random access memory' (RAM) it's got. Both are measured in gigabytes (GB).
Your tablet has got 1.5 GB of RAM if it's the version which can only connect by wi-fi or 2 GB if it can also connect to a phone signal. The more RAM you've got, the faster your device can process information. (So a tablet with insufficient RAM is likely to 'crawl' at times, especially if you're running lots of apps at once or you're doing things which use a lot of data, such as streaming video). 1 GB of RAM is probably the minimum which most tablets have these days but 1.5 GB or more is better. (As a point of reference, iPads have either 2 GB or 4 GB of RAM)
RAM is only used for processing data, not for storing it. That's the job of the hard drive (or solid state drive) in any type of computer. You need that drive for storing all of your apps on. You can also store documents, photos, videos, etc on it, so 'the bigger the better' is generally a good rule to work to. However most (all?) tablets let you add to the available storage capacity by inserting a memory card into them. (Your tablet allows you to insert a microSD card up to 128GB, vastly increasing the basic 16 GB it comes with).
You need to note though that while the extra storage space provided by a memory card can be used to store your photos and videos (etc), it often can't be used to store apps on. So if you expect to be needing loads of apps it's important to get a tablet with plenty of storage space on its internal drive to start with (rather than relying upon adding a memory card to it).
A really basic tablet might come with only 8 Gb (or less) of memory on its internal drive. Given that the operating system (such as Android) it uses will take up much of that space, it doesn't leave a lot for adding additional apps (and it's virtually useless for storing lots of photos and videos unless a memory card is added). However it could still be good enough if the user only wanted to use the pre-installed apps. 16 Gb is better. Unsurprisingly, 32 Gb or above is better still but things start to get rather pricey for such specifications.
If your OH only wants a budget (but reasonably well-specified) tablet, and doesn't mind not having full access to all of the apps on Google Play (i.e. he's largely happy to use the good range of pre-installed apps), he need look no further than the Amazon Fire 7. The price on Amazon.es is €69.99 for the 8 Gb version but it would probably be better to go for the 16 Gb one at €79.99. Alternatively, for a bigger screen, with a higher resolution, he could consider the Amazon Fire HD 8. That costs €109.99 with 16 GB or €129.99 with 32 GB.