This is a bike to sort out get out and ride.-----And enjoy. Don't think it will be worth spending a great deal of money on except to get running- but it will make a good bike. The gear problem could possibly just be derailler adjustment- or worn chainring or cassette- or it could be Bottom Bracket--Just no idea!!!
Upgrades? Not much but you might be wanting a different saddle- most of us would. Even changing the front Axle to a QR is not worth it- in my opinion- but you do currently have an Anti Theft device fitted there (Not many thieves carry spanners in their pockets)
Be honest and the bike is worth more than you paid for it. Spend the savings on getting it checked over- if possible by an experienced cyclist or possible take it to a shop for a quote.
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How long was I in the army? Five foot seven.
Spike Milligan