Sorry for the glitch on the post. This time I was able to access the entire posting you first sent in. A blown tire and high shaking can be really uncomfortable and a little scary and I hope my information will help keep this from occuring again.
One question is the fuel you use. I would reccommend using the same grade of fuel. It helps to use fuel from a Top Tier dealer because it has additives which keep carbon deposits from forming and your engine will run clean. Dealers in the fuel are Cheveron, Shell, Phillips 66 and some others.
As far as tires go, the best tires on the market are Michelins. They provide a good tire life and they use quality components when building the tires. The exact size and tread can be sorted out at the tire dealer. (So much depends on what your uses are that it is hard to cover over the internet.)
I was thinking about why the tire blew out in the first place. If the tire was 7 years old, it should have been fine. If the tire was low on pressure it can over heat and cause it to blow out on the sidewall. The little screw on tire pressue gauges are nice. They simply screw on to the valve stem and show green when the tire is at the correct pressue/ red when it is low. You can expect to have to add air to tires once a month. They naturally loose pressure due to permiation. I like to check the spare once a year to keep it in good shape in case I need it.
Also a old style of patch may have been put on the car. If a simple patch is installed it allows water in between the treads. This will deteriorate the treads and cause seperation and a tire failure. When patching tires be sure to ask for a plug/patch. This prevents water intrusion and tire failure.
If you park the car for long periods it will cause flat spots on the tires and some vibration is going to be apparent during the first 10 minutes of driving.
I hope this is helpful and answers you question. If you need more advice, please reply. If your needs are met, please select "accept".