A track pump - they're the big floor mounted pump with the handle on top. Don't skimp on this - something like one from Silca with an all metal barrel, sturdy wooden handles and a good gauge. The bike will roll much more efficiently when the tyres are pumped upto the correct pressure and sometimes folks who are just starting out are surprised at how hard the tyres are supposed to be. The pressure on the side of the tyre is usually the "max inflation" pressure - which isn't what you really want to ride at. For a 23mm tyre with a fairly big guy riding it then around 105psi front and 110psi in the rear would be a good starting point. If you start getting past 120psi on clinchers the ride can get a little bumpy/bouncy with not much in the way of additional rolling resistance reduction.
The best upgrades are often ones that directly involve the rider. If you haven't had one, a good bike fitting can often work wonders especially on the longer rider over consecutive days. Check on the British Cycling website for a coach that's local to you and give them a call on the dog 'n bone to see if they can get you set up with an efficient position on the bike.
After that it's good shorts, shoes, socks and shirt... not forgetting the mitts of course. Again, it's all about the rider and not about the bike... Doesn't matter if you're riding a $10,000 team issue bike or a jallopy from the tip but when things like the lower back, hands or feet start to hurt then things can just plain suck. If you can do a couple of 70 mile rides back to back and things are OK, I'd leave this until after the ride.
If you're fairly new to cycling and want to know more about how the bike works and how to adjust things then Shimano's website is full of good stuff. Unless you need really specialized tools for facing headsets or bottom bracket shells on a frame etc etc then there really is no need to take the bike to a bike shop for maintenance.
One thing I would recommened if you have a history of tighening down screws and bolts mighty tight - a torque wrench and a set of allen key sockets. Most of the stuff on a bike just needs to be snugged down and nothing more and much more than that and things can often break. The front deraileur clamp and seat post bolt are two big offenders for overtightening - handlebars/stem are next. 6Nm of torque really isn't a whole lot...
Shimano Tech Tips:
bike.shimano.comtech tips.htmlOpen ↗
Shimano Tech Docs:
techdocs.shimano.comindex.jspOpen ↗
The Tech Tips are basically overviews of how stuff works - it doesn't really matter if you have the bottom of the range dual pivot brake calipers as they essentially work the same as the Dura Ace top o' the line stuff without some of the bells and whistles. Same deal with the gears...
This book is a good read if browsing websites leaves you a little cold:
Zinn & the Art of Road Bike Maintenance
Leonard Zinn is the guy who posts on Velonews about bike "stuff" and maintenance issues. There used to be lots of good videos on maintenance up there.
Get some long rides in prior to the event. Aim for a couple of consecutive days of riding - weekends work good for this. As counter intuative as it sounds I'd get the bigger ride in the first day and see how you fair on the second. You've only got a month to go so time is of the essence...