Ok, I don't have enough info on your schedule to give a full workout regime but I can suggest some exercises that you can pick and choose from - always remember its good to mix up your routine, and to give it a complete makeover after every month of two. Because most of these don't rely on large weights, I would suggest maybe 3 or 4 sets of as many reps as you can manage, but its really a learning process so it might take a little while till you get a comfortable routine: (also a word of caution, do a google of any terms I use that you don't understand so that you don't injure yourself!)
Legs (quads) - one legged squats, working up to holding the dumbbells
Legs (hamstrings) - use your dumbells to do a straight legged deadlift
Legs (calf) - one legged, stand up on your tiptoes, hold and return, holding the dumbbells
NB. Legs are THE most important muscle in the body to build up.
Abs - any variation of situps and crunches
Lower back - Lying on your front, lift your upper body slightly off the floor using the back muscles
Chest and triceps - press ups or dips (there are also various individual tricep exercises that can be done with dumbbells)
Upper back and biceps - ideally get yourself a pullup bar, alternatively bicep curls and with the dumbbells try a one arm row
Final point to mention. You may think you're eating like a horse, but if you're serious about building muscle and are doing these exercises properly, you will need to eat more like a rhino!
I hope that helps a bit. Still probably best to contact some more professional advice but I've gained all this from a lot of research while I was losing about 5 stones of weight (while holding down a strat job so it is possible!). I realise compared to the usual topics on this forum I now sound like a total meathead, but I understand your situation completely (although slightly in reverse!) - I lost weight not to look like Arnie, but to get back to playing the level of squash I had been, and would describe my aim/what I achieved as an 'athletic' figure.
It takes effort, but good luck!