I need to change the belts and a fuel filter, any tips before I start.
Also, When I accelerate the car starts to shake, but when it is just riding with no gas it coasts smooth.

Be careful if the fuel filter is rusted. Spray it up good with WD-40 and DO NOT use adjustable wrenches to remove the nut.

I once had a Jeep that shook when I accerated. It turned out that I need new spark plugs.

Well you should check the recomended intervals to change the spark plugs. Is your care in such plateu(like the mielage to consider a spark Plucg change) and also like the Rom said. Change the fuel filter and do not use aadjustable wrenches. If you eat up the sides then it will be a nightmare to get it out.