A "Little" information on Shortwave Listeniing:

Shortwave listening is generally at its low point in the daytime hours (Mid AM to Late Afternoon localtime).
The higher bands are best in Daytime hours - 16, 19 and 22 Meter Bands being normally best.
You can give a try on 13M, 31m and 25m too.

Sunrise and sun set can be interesting on many bands that even goes for MW.

Nighttime gives more bands open - typically from 25m down thru 90m, with 49m probably being the best then 41 and 49 next up.

Even a modest SW Portable can pick up many stations some to consider would be:
Grundig/Eton G5/E5 Good for USB/SSB also even though no seperate USB/LSB
Sony 7600GR
Sangean 909 has 40Hc tuning steps and seperate USB/LSB switch (Not as sensitive as others)
Kaito 1103 and 1102

For a better Receiver the Eton E-1 is a good buy and has many great features.

The next up would be a Good Table Top the Icom R75 is hard to beat for the money.

A good Antenna is a very important part of SW radio - and even for portables. The lesser portables can get overloaded with to much signal strength from a good antenna, but a small amount of wire will help them a good bit. I am not getting into antenna's here you can look them up easily on the internet.
One site for serious projects is: http://www.hard-core-dx.com/nordicdx/antenna/

Main Shortwave Bands for Broadcast Listening:

Meter    Frequency

Band      Khz

120m     2300 - 2495
90m       3200 - 3400
75m       3900 - 4000
60m       4750 - 5060
49m       5900 - 6200
41m       7100 - 7450
31m       9400 - 9900
25m     11600 - 12100
22m     13570 - 13870
19m     15100 - 15800
16m     17480 - 17900
15m     18900 - 19020
13m     21450 - 21850
11m     25670 - 26100