Welcome to the site reeterry and congrats on your new lotty
First piece of advice, is to take photos of your progress. It's very easy to forget what you've achieved.
Then, don't try to do too much at a time. It's a good idea to try to get stuff in so you have something pleasurable to focus on as well as the hard work
If you click the Growing Help link underneath the top banner, you'll find a number of articles including how to clear a plot. This will give you some general guidance.
As for using glyphosate (the active ingredient in roundup), it's entirely up to you. You will need to spray it on a windless day to ensure no drift onto others' plants or plots, and ensure it doesn't rain for at least 6 hours after spraying.
It works on actively growing plants so should be OK on your weeds. Some may need a repeat application. You may still have to dig out some roots but it will definitely give you a chance of getting on top of the plot before it gets on top of you.
Once the weeds are cleared then continue to cover up behind you if you're not growing in that area, as the weeds will regrow.
This chart will give you some idea about what you can start off now:
http://www.allotment-garden.org/vegetable/general/sowing-harvest-vegetable-chart.phpEverything you've mentioned would be OK. Not sure about spuds though, because they might attract late season blight and potentially leave diseased material around for next season. If you use first early varieties you should get away with it - if you can find seed tubers. Don't just use ones from the supermarket.
Personally I'd leave the fruit until the autumn.