With a question like that it is very important to know what you intend to do with the recordings. Are you aiming to sell produce or just staying amateur..

You may not be there yet but any serious wildlife recording needs highly noise free equipement including preamps and mics and those don't fit with low budget... how does the tascam work for you yet, what do you dislike about it ?

In my opinion, if you go pro or semi pro, you should start with some mics to put on the tascam, once the recording is done, the software is kinda secondary, many can do the job including some free ones..

Thanks. Yes the first thing I am looking into getting is a shotgun mic. So far I really like the Tascam, it has really sensitive and clear mics. I don't hear the world the same way now, there is a lot noise. So far I have been recording in local parks which I have found out are all too close to traffic and airports. I made my own wind block cover that seems to work pretty good.
I want get more serious about it and get better, use the Tascam as a backup.

A shotgun mic is a great tool to pinpoint a source but not very good for ambiance sound. So if you want to go for a single bird, it's good but not for the whole forest...
The noises usually comes from gain staging and/or limitations of the unit. If your input signal is very low, you are bound to get a lot of noises when you push up the volume at mix time.
Noises could come from the environement, but when you record nature, which is sometime whisper like sounds, the mic quality and preamps come play. I would say that adding a mic to the tascam will give you better results but you would still use its preamps so 1 step up but not at the top yet.

For inspiration, you can research Dan Gibson which is one of the very successfull nature recordist.

Thanks again. The trip to the top is half the fun, I have learned quite a bit the last few days just by going and recording.
Finding a nice nature area away from modern life will help. In the mean time learning how to overcome the obstacles will be a big help.
Getting used to the equipment and finding out what it can and can't do will save me a lot of problems later.