Welcome to CoffeeSnobs [smiley=thumbsup.gif]. Your problems described above are mostly likely interrelated. In short, you need to get yourself a decent tamper, as you have alluded to, and where to get one? Well, right here from one of our sponsors, thats where. Just look up on the top L/H side of the page and you will see a list of sponsors, the one to go for is CoffeeParts.... they have a good selection.
From memory I think the Sunbeam baskets are 53mm I.D. but to play it safe, you should measure with a Vernier gauge or similar. Once you know the correct size, head over to CPs and have a look at their selection. I wouldnt go with anything flash or expensive at this early stage, since you will most likely get bitten by the upgraditis bug and will then need a different size tamper again. All the best,