You could also look at the Platinum range of bass strings from Newtone. These have a smoother wind than normal and you can also choose round or hex cores.
Add to your list Ashdown their older 15w with an 8" speaker is only £79 at a lot of online retailers. More than enough power for practice and I think Andertons have a video/youtube review of a number of practice amps.
With regard to pricing I have not found Amazon to be the cheapest recently in fact up to 20% dearer on some of the products I have been looking for. Also found their search engine throws up anything it thinks is close to what you want even when the part or product entered is specific, it's becoming tedious.
It's due to their construction. Being made from flat metal they do not attract dirt into the windings like roundwound so last longer.
There are many stories of pro bass players not changing flatwounds for years, decades even.
For funk listen to Larry Graham, Flea, Les Claypool, Marcus Millar and Stanley Clarke. Not all of these are out and out funksters but have been influenced by the genre.
A lot of practice combo amps have an auxilliary input for an mp/cd player that also allows a tablet or computer to be connected normally via the headphone or line out sockets.
Alternatively you could use a headphone amplifier like the valeton/vox or Blackstar which plug into the cable socket of the guitar and you just plug headphones in. If you are interested in going this route let me know as I have a spare unit that you could have which will allow you to concentrate on getting the bass first.
As per replies above regarding going along to a shop. Also try out long and short scale basses as well as different makes.
Best of luck on your bass journey.
Purchased a copy of Rivals of the Beatles book from Mick, easy process and excellent communication topped off by prompt delivery. A true Basschatter, many thanks Mick.