If you choose to SQ + separate LH ticket, you can choose the first/early flight to PRG (as SQ into FRA is hardly never late) but it would be way too risky/too tight to choose the late afternoon flight BUD-FRA. 1h15min at FRA is simply not enough when on separate tickets.

I can't tell you whether to choose the TK itinerary or the SQ+LH option. If you have travelled with SQ before then maybe it is time to try TK ? Most likely you will not be disappointed and you will have access to the fabulous TK lounges at IST both ways.