1) stock up like crazy (you probably don't have the TU for this yet)

2) See how much TU the quest will earn you and don't spend more than that while buying the items (always check the shop that the items would be in before going to user shops)

Now, the second method will likely not get you too high in the rankings on any quest, which means you won't get the greater rewards for higher tiers (the same request at level 1 will give far less TU than that request at level 45). However, it will boost your TU and you can start stocking up on those items so next time you can do method 1.

Also, invest in stocks. This can be a little confusing at first (and no, how the shop did that day does not affect how the stock will go so don't try to buy lots of stuff from the shop that you bought the stock in). My best advice is don't actually buy any stocks at first, see which go really high and really low, then buy low and sell high and poof, instant TU (and by instant I mean sitting around being VERY patient sometimes for weeks or even months depending on your stock).

Finally, play all the luck games and the skill and knowledge games that you can (egg count doesn't give much but it's good when you're starting out, word scramble and mystery item may be a little difficult if you don't know the items on the site but you might as well try, you don't lose anything by playing). Eventually you may get to the point where these games just aren't worth your time in terms of TU, but again, when you're just starting out these can be crucial to getting you over that edge where you have enough TU to make it through quests and stocks.