Advance rail tickets are already available for that period. Using Tuesday 18/07 as an example, outbound travel is available for £23.00 at 0700 from Temple Meads (arr. Paddington 0829) and 0800 (arr. 0934).
You can return from Paddington for £23.00 at 2000, arriving into Temple Meads at 2134.
Search here:
https://www.nationalrail.co.uk/
(NB: Do NOT use third party sites, such as The TrainLine. They can't find you any cheaper fares, they usually add on an unnecessary booking fee and they've been known to issue tickets which simply aren't valid for travel at all).
To travel around London, simply use your contactless debit cards to tap in and out at Tube stations.
If you're big kids at heart, the Science Museum is an absolute must. Note though that you MUST pre-book (free) entry to the museum and, to get the very best from your experience, you might well want to pre-book (paid) admission to one or more of the 'premium' attractions too:
https://www.sciencemuseum.org.uk/
(Note that a 'quick' look around the Science Museum will almost certainly take you at least two hours but many people spend four or five hours there. It's a big place, with lots to see!)
The Natural History Museum is just around the corner from the Science Museum, so many people like to combine the two. Advance booking is, again, essential, with most of the galleries being free to visit but with a charge being made for special exhibitions:
https://www.nhm.ac.uk/
The V&A is just across the road from the two museums that I've just mentioned. Admission is free (although some special exhibitions may carry a charge) and you don't need to book in advance:
https://www.vam.ac.uk/
The Shard is ridiculously expensive. The only time that I might consider visiting it would be for a 'special occasion' meal in one of the ridiculously over-priced restaurants there - preferably when someone else was paying!
If you're looking for somewhere cheap to eat in central London, consider Bistro 1 on Frith Street, Soho. Their three-course lunches, for just £16.90 are very good and amazing value too!
https://www.bistro1.co.uk/setlunch/