Agreed that for one man, if you can carry the bulk and weight of a two-man tent it's far better than squeezing into a one-man tent.
If you want weather tight, it's not going to be very cheap.
Cheap tents will usually shelter you from rain, but the groundsheets often fail badly. When I use cheap tents I usually put them on a sheet of polythene to help the groundsheet.
Recently I didn't bother with the polythene sheet when I pitched a cheap tent in France and things got very wet and muddy when groundwater soaked through the groundsheet.
You'd have thought I'd have known better by now.
With or without a tent I normally use a bivvy bag. It saved my bacon in France that night.
Don't bother with 'pop-up' and 'festival' tents.
Dome tents with a couple of flexible poles which cross each other in the middle are about the simplest to set up, and they usually don't need any guys if the weather isn't too windy.
Unfortunately the doorways on dome tents tend to catch a bit of rain, but you can get them with a porch although it adds complexity (and weight and volume). Tunnel tents tend to be better from that point of view but they'll usually need guys.
There are too many available to give a representative selection as examples, but I've had good service from Vango and Jack Wolfskin which are probably at the more expensive end of the range you'd be interested in.
Practice putting the tent up and taking it down a few times in daylight on the lawn or something before you do it for real at night in the pouring rain.
Make sure you know where everything is when it's stowed.
A tarp is a really useful addidtion to any tent setup, it gives you a lot more useable sheltered space for little extra weight and bulk.
