A+ is for technitions - with a degree and having done private work on PC's you should be able to pass that with no effort at all. cost's about 100 quid tho.
Network + is almost an extention to the A+ and i've been told it's designed for the network manager/engineer type job. again you shouldn't have any iissues with that with your previous degree.
A+ and Network+ are CompTIA exams - have a look at there website for other exams. there widely know about in schools and within the industy. some people love um, some dont care if you havent got them. the linux+, security+ and server+ look to be good ones to broaden your skill base as often they are just windows type exams. do look at working towards an MCSE. cos it will get you into a management position within a school easily. and tbh the spec isn't that difficult it's just - very microsoft! the cisco exams are rated by alot of people, and again there not hard, just time consuming. if your after tables of the money for each/what people want then tech republic have reports of the industry and it's qulifications
i dont know much about where you work or you but if you havent;
get a webserver and learn PHP/MYSQL and use it,
get an exchange server, use outlook and show SLT/SMT how they can use their calander and their PA's,
create staff training for those less abled colegues,
redesign the network with redundancy if you can,
get a VLE working,
learn how to use the phone exchange if you have one, create a VOIP exchange if you havent got one,
learn how to use power tools. install whiteboards is a good one. and learn how to wire patch cables ect...
learn opensource ways of doing things - i'm assuming the school will be very microsoft. saving cost is always a good thing in schools or buisness. having a degree i'm guessing you'll have used alot of open source stuff alreddy.
alot of those who are managers are in positions where they do not just manage computers - often the MIS, echange, e-mail, website, tv, dvd, whiteboards and phones come under the role of network manager. in schools anyway.
btw i'm in the same position as you somewhat except i dont have a degree to my name. 19 working in a school, trying to absorb as much as i can to broaden my skill base before moving to somewhere else/get a promotion. i went the experiance root and did volentry work there one afternoon a week for 6 months. then didn't for a year, concentrated on my a-levels at a different school, as part of that i set up my own domain/group policies ect, own e-mail server, and application server (running vmware, iss, apache, mysql php and microssoft sql) rote a few little web apps, then the post came up, me vs 11 others. i got the job beating people with degrees and those who had been in the industry, even network managers. probably cos i was young (just 18 then), enthuastic and had the relevent experiance they were after. and they knew my skill set cos i had proved it through the volentry work then what i managed on my own. now i'm not really bothering with exams cos i dont rate them. i will be doing an MCSE when the 2008 one appears if it does cos that what i work on at home/experiment on. my boss (net man) reckons an A+ would be easy for me so i may do it when i have the spare day or two to revise, and he's also working toward an MCSA.
use monster and other job search engines to look at job descriptions and try to meat all of them. if you can do that then you'll be well on the way to having everything u will need for future jobs.