How big inverter/UPS should I buy?

Short answer: the model you choose depends on the watts of what you want to run. We recommend you buy a larger model than you think you'll need totally (at least 10% to 20% more than your largest load).
 
Completed answer: when determining continuous power and surge (peak/starting) power, you need to consider how much power do your devices require to start up (surge power), and also the continued running requirement (continuous power).

What is meant by the terms of "continuous 2000 watts" and "peak/surge 4000 watts"? Some devices with motor require an initial surge of power to start up ("surge power" or "peak power"); once started, they require less power to continue to operate ("continuous power").

 
To calculate approximate surge power:
 
    Watts X 2 = Surge power
 
This formula yields a close approximation of the surge power, though some may require even greater ones.
 
Note: induction motors such as air conditioner, refrigerator, freezer and water pump may have a start up surge of 3 to 7 times than the continuous ratings.
 
The below tales are general rated power of some home devices, the induction motors are marked with *.
 
 

Appliance
Estimated watts
Appliance
Estimated watts
Coffee pot (10 cups)
1200
VCR
40-60
Coffee pot (4 cups)
650
CD or DVD player
35
Toaster
800-1500
Stereo
30-100
Cappuccino maker
1250
Clock radio
50
Coffee grinder
100
AM/FM car cassette
8+
Blender
300
Satellite dish
30+
Microwave (600 to 1000 W cooking power)
1100-2000W (elec. consumption)
Vacuum cleaner
300-1100
Waffle iron
1200
Christmas lights (50)
25
Hot plate
1200
Space heater
1000-1500
Frying pan
1200
Iron
1000
Toaster oven
1200
Washing machine
920
Blow dryer
900-1500
12" 3 speed table fan
230
Computer
- laptop
- PC & monitor
- printer-inkjet

50-75
200-400
60-75
TV - 25" color
- 19" color TV or monitor
- 12" black & white
- 13" color TV/VCR combo
300
160
30
230
*Refrigerator/freezer
600
Game console (X-box)
100
*Freezer
500-800
*Furnace fan (1/3 hp)
1200

 
Common tools:
 

Tool
Estimated watts
Appliance
Estimated watts
Jig saw
300
1/4" drill
250
Band saw
1200
3/8" drill
500
Table saw
1800
1/2" drill
750
6 1/2" circ. saw
1000
Shop Vac 5 hp
1000
7 1/4" circ. saw
1200+
*Sabre saw
500
8 1/4" circ. saw
1800
*Portable grinder
1380
Disc sander
1200
*Electric chain Saw 14"
1200
Makita chop saw
1550
*Airless sprayer 1/2 hp
600
Makita cut off saw
1000
*Air compressor 1 hp
2000

 
Pumps and air conditioners:
 

Pump
Running
Starting
Air conditioner
*Well pump 1/3 hp
750
1400-3000
*7000 BTU to 10000 BTU
Running: 1000-1500. Starting: 2200-5000.
(A/C's are a very difficult load because of the high start-up surge. Use the locked rotor amps to determine the start up surge requirement).
*Well pump 1/2 hp
1000
2100-4000
*Sump pump 1/3 hp
800
1300-2900
*Sump pump 1/2 hp
1050
2150-4100

 
Note: the wattages given above are estimated, the actual ones required may differ from those listed. Check the nameplate to determine the actual wattages required.