There are novice level spells available for sale for all of the magic schools. The best place to get them is Edgar's Discount Spells in the IC Market District. He sells at least one novice level spell from each of the magic schools (many of the same ones that you get as starter spells if the school is a major skill). You have to get something that's cast on self, so that you always have a valid target so you always get experience for it, and with most of them, you can just keep casting them over and over 'til you run out of magicka, wait to recharge, then do it again. The basic ones are Protect for Alteration, Minor Life Detection for Mysticism and Starlight for Illusion. For Restoration, you already have Heal Minor Wounds, though you can get Minor Respite from most of the Temples, and it has a lower cast cost. For conjuration-- the only novice level conjuration effects that'll work as trainer spells are some of the bound items. You can't cast the spell again until the first one has worn off, so it takes longer to train it, just because you have to cast it, then wait 15 or 20 seconds for the bound item to disappear before you can cast it again. I generally practice conjuration while I'm traveling from one town to another. Edgar sells Bound Dagger and Calindil at the Mystic Emporium sells Bound Helmet. Bound Dagger has the lower cast cost, and it only lasts for 15 seconds as opposed to Bound Helmet's 20, so it's a bit quicker to train. If you wait until you get to Chorrol, Alberic Litte sells Bound Gauntlets, which has the lowest cast cost of them all.
Destruction is the only one that you can't train until you get to the AU, just because there are no premade cast-on-self destruction spells. Once you get into the AU though, you can make a cast-on-self weakness to one of the elements.
And it is handy to get into the AU and do custom training spells for all of the schools. I always do a full set-- one for each school-- of the minimum time for the cheapest effect. They generally have a cast cost of 1, so you can cast them endlessly. And they're incredibly cheap to make (generally 3 gold apiece).