Yeah, that's what difficult about real languages.
I was surprised myself when digging through wikipedia I found that Russian has OVER 15 VOWEL sounds, just like English. Only in English most of them are considered "different" and important to distinguish between words, while in Russian all of them are variations on standard А, И, У, Э, О, Ы.
See, in "весь" the E is sandwiched between two soft consonants. Remember what I said about palatalization, and how your tongue is raised? Well, this has effect on vowels as well as consonants. When your tongue is raised for palatalization, Е in "весь" becomes more "closed" vowel than in "лес" or "это". That's the same reason you have A from English "cat" in "пять" or "мяч". Normally Russian А sounds quite different from English A in bad/cat/map/lap.
However, you shouldn't worry about such peculiarities unless you are a speech synthesizer. For real er... mouth and tongue these variations occur naturally: for instance, "лес" has a vowel like E in "bed" and "весь" has a vowel like "eh" in "play". You may have hardly ever noticed that they were somewhat different in quality. Still, as IPA chart says, they areI only linked you there because the page has explanations of how Russian sounds may be different. And each vowel/consonant sound has its own page, where you can listen to it, get an overall idea where the tongue is, how the sound is generated and, for example, whether you have this sound in English or not, or maybe only in dialect you don't speak.
Try using forvo.com or some recordings and... well, copy! If you can already pronounce words, it usually doesn't take much time to at least obtain your own pronunciation (save for R, which is difficult). Maybe, imperfect pronuciation - hell, you are gonna have an accent, and won't get rid of it in near future! Yet, for a beginner "good enough" is when you hear the difference between sounds (ok, лук "bow/onion" and люк "hatch, manhole") and can use them in your speech. To some extent, of course.
If you want my opinion, your major obstacles are going to be:
- lack of "normal" Russian A in English. I mean, certain realisations of A do exist in English, but how you say "Aaaah" in English is a bit different from how I say "А-а-а" in Russian. Same with "O", sadly. But don't you worry, sounds in "Aah" and "law" are a good thing to start with.
- in English vowel sounds are less variable depending on their environment; as a side effect, when you try speaking Russian as English, it sounds, well, strained, Relax, Russian vowels are subject to much allophony
- Ы. You don't have that
- Р, which is different from English R (which is absent from most major laguages, anyway). Don't worry, even children have some trouble mastering this sound. I started consistently pronouncig it correctly, different from L in both hard and soft variants, from the age of 7 or 8. Even in words like секретарь
- X. Way easier that Р, as you don't have to do anything complex with your tongue.
- palatalization. To make things harder, a few sounds have other changes when palatalized: for example, л in люк is close to L in "loop" (i.e. alveolar), while Л in "лама" is not.
- no real air "puffs" (aka aspiration) in K,P,B
- T,D,N and hard L are pronounced different: your tongue touches your teeth (or almost touches)
- Ш and Ж are retroflex (tongue tries to slightly bend backwards as compared to straightforward English SH). Щ is even more hissy than English, and, in fact, it's a double consonant. If you want half Щ, Japanese have it.
- Ч is close to CH, but is, so to say, palatalized. Your tongue is raised even higher than in English
- consonant clusters. And consonant clusters with palatalization. Sometimes two adjacent letters get softened, but the overall tendency is not to - for most clusters. I.e. it's an actual process noticed in the language, as consonant system gets more complex and vowel system simplified. For example, in стена "wall" I only pronounce T soft, while C remains hard ("both soft" is still an acceptable variant, and was a mainstream one, like, 50 years ago).
- devoicing of consonants and reduction of vowels. Пароход "steamboat" is pronounced the same as if it were парахот.
- and, actually, stress is different. Russian stressed syllables are not only louder, they are a bit longer.