Ideas for upgrades that i would personally consider: better pedals, better brake pads, complete cable rewire (both brake and gear cables) maybe new tyres depending on how much life is left in them. Also you mention straight bars, that's all well and good but if you did want to change the bars then you're certainly going to need to change the stem and brake levers, and more than likely the headset too (going from what i can see in your dark, blurred pic) so for ease and cost effectiveness, i'd suggest you just get new bar tape and learn to get comfortable with the bars and setup you have.

How au fait are you with bicycle mechanics and maintenance? If it's not been serviced for a few years a complete strip and re-grease would be recommended, as would probably a new chain. and if the bottom bracket (the bit between the pedals) makes any noise i'd get that seen to asap.

But as far as actually doing 'upgrades' are concerned, ride it and see what you want to change about it, no point changing things that don't need to be changed.

I think the bottom bit between the pedals may be called the crank not the bracket ( that is if I'm au fait with mechanics )