For learning/home practise, if you have to ask the question, first qualifier is definitely a solid-state combo something. i.e. Anything tube is out.
40W or less is ample.
Like the guitar, it depends what you want to do with it (yer I know practise at home) i.e. record or just play, and what you want to play. What guitar do you play, and what style will most interest you after you have finished Fundamentals 1 & 2. i.e. You woudn't buy a Mesa Boogie II if what you wanted to effect is The Beatles early Vox AC30 tones.
How budget orientated are you? Got a price point in mind, or just what you like/want with no limit?
[br]The usual list of popular combo contenders. Whether you want progammable e.g. downloadable flash capable aka patchable or simpler selectable WYSIWYG loaded onboard modelling, or modelling at all, is up to you. Nearly all SS home practise amps in this category these days feature modelling.
Yamaha THR10
Fender Mustang GT 40
Fender Champion 40
Boss Katana 50
Blackstar ID:Core 40
Peavey Vypyr VIP 2 40
Line 6 Spider V 30 (next up is 60W)[br]Marshall Code 50
Vox VT40X 40
Boss' Katana 50 is probably the sweet point, and is a very popular amp. Hard to go wrong buying it. I also really, really like the KISS simplicity and tones of Fender's Champion 40. Another different demo, cleaner tones orientated. I later bought their Champion 100 and I really love it too, but it is overkill -understatement, for practise at home use.
Out of the above, I use Blackstar's ID:Core 40. I agree about the Fender Mustang GT. I seldom use the patching feature of the ID:Core, and I'd really rather play than fiddle endlessly with every feature and effect with it.
For recording I use either my U-Phoria UMC204HD audio interface into a DAW, or an amp simulator, so the ID:Core's USB feature ends up being a redundant feature, although it would be useful if not going down the path of buying an AI or AS.
The choice is endless. Don't overanalyse it. At some stage you just have to dive into the water. Just buy the one you can afford, you like the sound of - You Tube demos will give you a pretty good idea, with the feature/s you will actually make use of. You can always change later.
If I was to kick off again knowing what I know now, I'd probably buy Fender's Champion 40 as my first amp by choice. Alternatives would be either the Boss Katana 50 if money didn't factor into the equation, or the Blackstar ID:Core 40 if it did. I bought the ID:Core and could afford to also buy the Fly 3 Combo Pack which included the Fly 103 cabinet & PSU with the difference in price between the Katana and ID:Core.
P.S. If I only had one home practise amp, I'd choose from one of the above, or a 20W version if 40W isn't required. As I don't, I also have a Blackstar Fly 3 which I find myself using a lot of the time because of the anywhere convenience of its battery independence and small form factor portability. Plus it's infinitely more neighbour family friendly for multiple sessions everyday if you don't want to use a headset - although you still can with it (& it has MP3 backing track input). Boss' Katana Mini is a similar alternative. Both impressive mini amps for their outputs.