I found a trick years back. If you keep the tax collectors gold when asked by gramps, kill the perpetrator anyway, and then chat to the Census and Excise bloke once more, he gave me the bounty for taking care of the murderer, despite me lying about finding gold on his body. However its been about 4 years since I did this trick and I'd imagine it got patched by the Morrowind Patch Project.
Also if you want a real good boost at the start, go to the guard towers in Ald'ruhn quickly and loot the entire bonemold armour sets in the crates.