Here is what I do. I grocery shop 3-4 times a week on my bike. It's usually on my way home from somewhere, so it's convenient. I can only carry what my pretty-big bike bags hold. This is just as well, so my produce doesn't rot in the fridge. I buy whatever looks good in the produce section, so things like:
berries, grapes, cherries, peaches, plums, watermelon, cantaloupe, honey dew melons in the summer; figs, apples, pears, in the Fall; apples and oranges in winter; grapefruit in spring; and the imported things from around the world while still affordable: avocados, bananas, mangoes.
Then the veggies: In the summer, we get lots of local leafy greens: kale, collard greens, mustard greens, and veggies: broccoli, zuchinni sweet corn; in the fall and winter: carrots, beets, potatoes, sweet potatoes, broccoli, cauliflower, rutabaga, lots of greens still. the list is huge. Get what looks good today, hopefully local and organic. Don't get too much so it doesn't go bad. After a few weeks you'll be able to judge how much you can carry if you are on foot or bike, and how much is too much if you have a car and it sits in your fridge for too long.
flavorings: onion, garlic, lemon, lime, ginger, herbs.
Then in the bulk section: raw cashews, walnuts, brazil nuts, almonds, flaxseeds, hemp seeds, dried lentils and beans, rice, oats..
then in the frozen section: frozen berries, mangos, cherries, peas, corn (unless it's fresh corn season!), edamame (unless fresh).
If I have a recipe in mind, of course I buy what's in the recipe. I compile a grocery list as I run low on staples, such as nuts and seeds, beans, etc.
Then I cook them all up or make smoothies or sauces. My "recipes" are often just combinations of whatever I have in my fridge.
The fruit is often unripe when you buy it (things like, peaches, plums, mangos, bananas, cantaloupe). So let it ripen for a few days in a fruit basket. You'll learn after a while how long this takes. It varies with the fruit. This does not apply to oranges, apples, and berries, which should be refrigerated and best eaten right away. Bananas are ripe when they start getting little brown spots on them. Then they are sweet, yum. I've done a side-by-side comparison and organic do taste better. I buy lots of bananas, and when they ripen, I peel each one, break it into about 4 pieces, put it in a ziplock bag, and throw it in the freezer.
Let's say you don't live close to the super fabulous organic store with raw nuts and date sugar. If there is one somewhere in your vicinity, you can go there once every month or two and stock up on the raw nuts (which you then freeze) and date sugar (a healthier replacement for sugar) and dates. Or you can order online, e.g., at organicfruitsandnuts.com
Hopefully your local store has organic produce. It is usually better tasting, better for the environment, and was better for the workers who grew it for you.
Equipment: The one thing I highly recommend is a high-quality high-powered blender. Unfortunately these cost a lot of money (though it costs a lot less than prescription medications that you can stop using when you eat healthy). I recommend the Vita-mix. The cheapest one is about $400 new. I have that one and it works great. It will blend anything, and the damper thing works great for smashing things down to the bottom to make them blend. You can make so many fabulous healthy low-fat desserts, soups, sauces, dressings this way.
Oh, I kind of like my food processor too. I'd go for the moderately price ones, not the super cheapo like my aunt has--that is a piece of crap.
Then I have become a recent convert to adding carrot juice to soups, so I recommend a juicer. I think you can get by with the cheap ones for doing carrots. Oh, and I have a citrus juicer too.
Another somewhat useful item which is affordable is a food scale to measure weights. It's useful for measuring nut portions. Nuts are high in calories and fat, so you should only eat 1-3 oz of nuts a day (1 if you are trying to lose weight, 2 if you are normal weight and activity level, 3-4 if you are very active or trying to gain weight). You can also weigh spinach amounts for your smoothies if you want. It just comes in handy. But it's not necessary. An ounce of nuts is about a handful.