Given your low budget, priority for me would be to have the gear needed to get going after a road side problem, followed by maintenance tools so you can do as much work as needed yourself. Then add stuff that makes life easier.
Roadside repair kit includes: Pump Tire levers Spare Tube Puncture repair kit Multitool - Cheap ones will fix many road side problems, but if its going to be used for regular maintenance get a better tool. Many multi tools come with tire levers.
Pump - CO2 is out - expensive to use - a puncture could eat your weekly budget. Smaller is better when you don't need it, bigger is better if you do. If you are going to have just one, rather than a mini pump get something like the Topeak MiniMorph. If you are getting a full size floor pump later, or have access to a floor pump though work or friends, get a medium sized mini pump, As this would be a road side only tool, a cheaper (not too cheap) one would suffice. Above about $20 your paying for weight and brand.
Floor pump A floor pump (ideally with a gauge) is very handy. You can get by without one, but they are no expensive - can probably get an adequate one for $20.
"Workshop" tools Your road side tools will do most regular maintenance, but don;t expect too much from cheap tools so get better quality if you plan to go down this path. Otherwise the best option would be a cheap "Bicycle repair kit" with most of the tools you need for price of one workshop quality tool. These kits do an OK job as long as you accept they have limits and avoid using them like a "Gorilla with a spanner"
Bike shorts. I strongly suggest getting a quality pair of padded bike shorts. Don;t need to be the most expensive, but don't go too cheap.
Ask around work and friends and let people know what you are up to. You may be surprised how many people offer to lend you their spares of many of these things. You may get lucky find someone has a perfectly serviceable road bike their wife/mother/son has not used in years......
See if you town/city has a bike coop / recycle yard. Many of these places have tools (and people to show you how to use them) so you can do you own maintenance.
Consider used bikes - many are hardly used, or good ones can be well used but very well maintained. tricky problem is identifying them. Talk to your LBS - they may be able to help with selling you a used 'trade in' bike.