Hi OP. Leeds dweller here.
Both of those houses are in typically 'bad' areas but they're not too bad to be honest these days. Not the best, but absolutely fine for getting on the ladder. I know some people who have lived in both of these parts of Leeds and brought up children there and have never had any issues.
More typically affluent areas would be kirkstall, chapel allerton, horsforth, headingley, alwoodley, Moortown, but like everywhere there's good and bad there too and sometimes the 'bad' parts of these affluent areas are worse than in the bad areas as they get less funding and support.
I'd recommend considering armley, kirkstall, burley, meanwood and potentially hawksworth (has improved muchly in recent years and isnt the hellhole some people think it is). There's good and bad in each, some streets wil be fine but the next street over will be bad, you'll get a vibe when you go and view. These locations all have OK access to the city centre and burley, headingley, kirkstall and horsforth have train stations with trains into town.
Honestly though i would recommend visiting some areas since, although leeds is very compact, the different suburbs all have quite different vibes and you need to get a feel for what would suit you.